## Thomasrauscher.ch

**PROBING DARK ENERGY WITH SUPERNOVA SEARCHES**
*CENTRA – Centro Multidisciplinar de Astrofísica, Instituto Superior Técnico, Lisbon*
**Abstract. **Four years ago, two teams presented independent analyzes coming from photometry of

type Ia supernovae at various distances. The results presented back then shook-up the scientific

community: the universe is accelerating with a positive repulsive fluid sometimes called dark en-

ergy. No significant work has disproved the fundamental results, yet some doubt subsists in the

assumptions behind the full use of type Ia supernovae as perfect distance indicators. The uncertainty

of the evolution problem, the explosion mechanisms and the diversity of the observed light curves

properties are often cited problems. All these aspects are now being deeply investigated in to-come

or already started supernova searches along with the on-going quest of determining the nature of dark

energy. We will present here a brief introduction to the use of type Ia supernova in cosmology, the

current status of supernova cosmology as well as an overview of the wide supernova surveys about

to begin.

**Keywords: **supernovae, dark energy, cosmological parameters

**1. Relating Energy Densities with Distance Measurements**
Measuring distances in the universe is a crucial step to get estimates of cosmolo-gical parameters. The greater the distances are, the more they give us access to thegeometry and the evolution of the universe. Several ideas to get good cosmologicaldistance indicators have been attempted since 1930. Whereas for nearby objects,there exists a variety of distance methods, for more distant objects, one type ofastrophysical object has been successful in converting redshifts to Megaparsecswith some good accuracy: Type Ia Supernovae (SNIa).

Two observations are needed to be able to use SNIa as cosmological distance
indicators: the spectrum gives us the redshift

*z *and the identification of candidate,and multi-band photometry to reconstruct the lightcurve

*F (t) *of the supernova.

Relating the two observations is done through the

*luminosity distance dL *arisesdirectly from the inverse-squared relation

*F (t) *=

*L(t)/*4

*πd*2

*(z)*, where

*L(t) *is
the intrinsic luminosity. The cosmological parameters are only included in

*dL*;supernovae observations are therefore ‘cosmological-model-independent’. So far,observations have not shown any other dependence of

*L *but the SNIa epoch

*t *andlightcurve shape parameters, conveniently removed after a standardization process(more on this topic).

With only two fair assumptions of an isotropic and homogeneous universe at
very large scales, and Einstein’s gravity dictating the energy transfers with geomet-rical properties, we can describe how the energy content of the universe influences

*Astrophysics and Space Science ***290: **1–12, 2004.

2004

*Kluwer Academic Publishers. Printed in the Netherlands.*
its single expansion factor

*a(t)*. Redshift is interpreted as a cosmological effectthrough the relation

*a(t) *=

*a*0

*(*1 +

*z)*−1. Each component of the universe can berepresented by a fluid of density of energy

*ρi*, where the

*i*-index represents non-relativistic matter (m), radiation (r) or dark energy (x). The values of the energydensities rule entirely the time dependence of the expansion factor, by the so-calledFriedman equation (see e.g. Peacock, 1999):
where we define the Hubble constant

*H *, and

*k *= {−1

*, *0

*, *1} a constant defining thespace curvature of a simple topology (respectively open, flat and closed) Universe.

At a critical density

*ρc *= 3

*H*20 where

*i *=

*ρc*, the universe is flat. For lower
values, of the sum, it is open. We further reduce the energy densities as

*ρi *. Given these notations, and defining
At present, observations show that only the matter and dark energy componentsare significant, and possibly, as indicated from all latest CMB data (Benett et al.,2003), we could live in a flat universe, leaving simply
Generally we characterize each energy component of the fluid universe by the
equation of state

*pi *=

*wiρic*2, where

*wi *is the equation of state parameter. We canassume very confidently at many scales that matter behaves as an ideal fluid suchthat for

*w*m = 0 for non-relativistic matter and

*w*r = 1

*/*3 for relativistic matter andradiation. It becomes less intuitive with the introduction of a repulsive component

*w*x

*< *−1

*/*3, as indicated by observations, very hard to test at laboratory scales.

There has been a very extensive literature dealing with the consequences or thenature of a positive, possibly evolving dark energy component. The cosmologicalconstant
is the most simple one. Often referred as a vacuum energy, it could
be the relic of some superseding theory. The equation of state parameter keeps aconstant value

*w *= −1, but recent development introduce a scalar field as a darkenergy component, with a

*w*x

*(z) *evolving with time (see Padmanabhan, 2003 for areview). We will see how it may be possible the reconstruct the equation of state,and we will adopt a first order parameterization

*w*x

*(z) *=

*w*0 +

*w*1

*z*.

Armed with a cosmological description, we can now derive the luminosity
distance. It is fairly straight forward to show the following formula (see e.g. Pad-manabhan, 2003):

PROBING DARK ENERGY WITH SUPERNOVA SEARCHES

*Figure 1. Left panel: *Luminosity distance as a function of redshift for various sets of

*( *m

*,*
at a redshift of

*z *∼ 0

*.*3 and above we can start to discriminate models.

*Right panel: *Degeneraciesamong various cosmological models assuming a flat universe. The combinations of

*( *m

*, w*0

*, w*1

*)*are compared to a

*(*0

*.*3

*, *−0

*.*7

*, *0

*) *model (Linder and Huterer, 2002). The

*w *in the figure correspondsto the

*w*1 in the text.

*i (*1 +

*z )*3

*(*1+

*wi ) *−
where S

*(x) *= sin

*(x)*,

*x *or sinh

*(x) *for closed, flat or open models respectively.

Somewhat complicated, the integrand is nothing less than the inverse of the Hubbleconstant at redshift

*z *and has an analytical primitive for a flat universe. Figure 1represents the luminosity distance as a function of redshift, for four different sets of

*i *’s. Only for redshifts higher than

*z > *0

*.*3 it is practically possible to discriminate
When we measure supernova fluxes, we have direct access to

*H (z) *and thus

*i *, but it causes degeneracies between
Even for pure standard candles, breaking the degeneracy among the full set of in-volved cosmological parameters

*(H*0

*, *m

*, *x

*, w*0

*, w*1

*) *requires additional inputs.

Typical additional inputs if we are interested in the equation of state parameters,are assuming a flat universe (from CMB), a prior on
and marginalizing over

*LH*0. Figure 1 shows the difference in magnitude expec-ted between a flat universe at
m = 0

*.*3,

*w*0 = −0

*.*7 and

*w*1 = 0 with other
m ∼ 0

*.*3. Nonetheless, to make supernova results as
independent as possible, it is very crucial to obtain a large set of well observed
and well redshift-sampled supernovae up to a redshift

*z > *1

*.*5. Multiple redshiftobservations brings more leverage and important degeneracy breaks between thecosmological parameters (Astier, 2001; Goliath et al., 2001; Linder and Huterer,2002).

**2. Current Results**
Obtaining a set of supernovae at various redshift is a dedicated task, on whichtwo teams have concentrated their efforts for the last decade. We present theircurrent results here. SNIa only appear few times per millennium per galaxy and canbe photo-metered for about 200 days in rest frame at low-z. Hunting supernovaerequires both a wide field and large mirror to cover a large volume of space, gettingmillions of galaxies up to redshift of

*z *∼ 1 from ground. A full discovery strategyhas been set up through the nineties by the two collaborations. The use of 4-mclass telescopes with the appearance of high quantum efficiency CCDs allowedsuch discoveries. Since a SNIa rises in about ∼ 20 days from undetectable lightto maximum light, the strategy elaborated was to use a 3 weeks baseline betweenmoonless reference images and discovery images of the same fields, and look forSNIa candidates in the subtracted images, using fine-tuned image processing soft-ware. Candidates were whereupon confirmed spectroscopically in 8m-10m classtelescopes and followed-up photometrically in as many telescopes as allocated tobuild the lightcurves.

2.1. DIMMING OF SNIA WITH A DARK ENERGY COMPONENT
Perlmutter et al. (1999a) presented cosmological parameters estimations from ananalysis of 42 high redshift SNIa, combined with 18 low redshift ones from theCalan-Tololo campaign (Hamuy et al., 1996). The observed apparent luminosityshowed a systematic dimming compared to a simple
which after careful checks, was interpreted as a clear evidence of a presence ofdark energy. Riess et al. (1998) showed very similar results from completely in-dependent analysis, from 10 high redshift and 27 low redshift SNIa (within whichthe Calan-Tololo ones). If we assume the universe is composed of matter and acosmological constant, the combined results show the existence of a cosmologicalconstant with 99.9% confidence leading to an accelerating expansion. Figure 2show the combined confidence contours for
By now assuming a flat universe, and combining measurements, with redshift
m and CMB measurements, we can get some limits on the
equation of state parameter. The constraints only suggest

*w*x

*< *−0

*.*5 – see e.g. Per-lmutter, Turner and White (1999) – and yet neither permit to discriminate amongdark energy models, nor permit to reconstruct a dynamical equation of state.

The statistical uncertainties are still the largest contribution to the total error
budget, although the systematics are not far behind. With a larger statistical sample,

PROBING DARK ENERGY WITH SUPERNOVA SEARCHES

*Figure 2. Left panel: *Combined confidence contours in the

*( *m

*,*
SNIa results (Wang, 2000).

*Right panel: *Equation of state parameter (assumed constant in

*z*) and
confidence interval, for a flat universe from (Perlmutter et al., 1999) results.

improving the current measurements would definitely require much better controlover the systematic uncertainties. Extensive internal checks have been performedon the properties of the high-

*z *and low-

*z *objects used in these measurements inorder to detect difference in the samples. We find that systematic errors are mostlydue to our limited knowledge of SNIa photometric and spectroscopic behavior.

Indeed, when measuring distances using SNIa, we apply corrections for instru-mental (e.g. k-corrections) and foreground effects (extinction). The accuracy ofthese corrections depends heavily on our knowledge of SNIa intrinsic properties.

At the moment, a half-dozen significant systematic errors have been identified. Wewill present the most important ones below.

The dimming of SNIa diminishes down to ∼ 0

*.*28 mag at

*z *∼ 0

*.*5 compared to anopen universe with
= 0, and several attempts have accounted the
dimming for other reasons but the distance. Apart for non-standard cosmologicalmodels, a more direct and physical explanation is to reconsider the assumptionsbehind the use of SNIa.

*SNIa standardization*Supernovae Ia explosions are short events and somewhat rare. They are likely to bethe result of a thermonuclear burning of iron elements of a degenerate CNO whitedwarf. The interest of SNIa in cosmology comes from the homogeneity in theirspectra and lightcurves. Although the homogeneity does not appear so strongly fortheir absolute magnitudes, a lightcurve shape analysis shows an empirical relation

*Figure 3. *Lightcurve of nearby SNIa in absolute

*B *magnitude. We can clearly see the dependencebrighter-slower. Brighter lightcurves are actually also a bit bluer (Regnault, 2000).

between the width of the lightcurve and the maximum luminosity, so they can beused effectively as standard candles. For a detailed review of SNIa properties, seeBlinnikov (2003) and references therein.

From accurate photometry, we derive lightcurve properties. With a full selection
of observed SNIa, the dispersion at maximum in

*B *and

*V *reaches

*σ > *0

*.*25 mag.

But removing a few extraordinary spectra and lightcurves from the set, we note aclear shape resemblance, as shown in Figure 3. As it can be seen, the slower su-pernovae are also the brighter ones (also bluer). This empirical relation has not yetfound a satisfactory quantitative answer among radiative transfer models, althoughmost of them suggest the phenomenon depends on the 56Ni mass. The temperatureincreases with the abundance of 56Ni, accounting for the brighter events, but alsoincreases the opacity. Photons are trapped for a longer time, accounting for thewider lightcurves.

To characterize the brighter-slower relation, several parameterizations are avail-

*m*15 representing the decrease in magnitude in the

*B *band 15 days
following the maximum brightness (Phillips, 1993), the ‘stretch’ of the time-axisof a

*B*-band template light-curve (Goldhaber et al., 2001; Perlmutter et al., 1997),or the
parameter of the Multi-Color Light Curve Shape (MLCS), a method using
a trained template to correlate simultaneously all colors and absolute magnitudeswith a single varying shape (Riess, Press and Kirshner, 1996). The reader is referredin Leibundgut (2003) for a critical overview of standardization of the SNIa lightcurves. Each method has its own application, and lead for all cases to an effectivepeak magnitude dispersion of

*σ < *0

*.*2, which translates into a dispersion on thedistance of about 7%.

PROBING DARK ENERGY WITH SUPERNOVA SEARCHES

*Extinction*Supernova light can be dimmed by dust present in the optical path. Roughly 10%of them show significant extinction. Extinction is color dependent: dimmed ob-jects appear redder and the total absorption is proportional to the reddening. Givensupernova intrinsic color, we can correct for reddening. Aguirre (1999) pointedout reddening dust is not the only one and suggested that intergalactic ‘gray’ dustexistence is not ruled out. It could be expelled from galaxies, and its possibly largegrain size (

*> *0

*.*1

*µm*) could produce a very small reddening effect, undetectable onthe current observations.

Two possibilities are explored today to measure the importance of gray dust.

The first one by taking multi-band photometry to increase the color leverage andmake the gray dust more detectable. A first attempt, though not yet conclusivewas preformed on one supernova (Riess et al., 2000). The second one is simplygoing at higher redshift to discriminate between scenarios of gray dust or darkenergy. Again, a first attempt at

*z *∼ 1

*.*7 based on a single supernova with onlyphotometric measurements (Riess et al., 2001) do not show compatibility with agray dust universe.

Finally one must not forget that dust correction from our Galaxy is subject to
uncertainties and going at higher redshift means going redder and thus less affectedby the Milky Way dust. Such a systematic error is today estimated as ∼ 0

*.*06 mag.

*Evolution*Differences in SNIa do exist. Intrinsic dispersion of lightcurves, colors or spectrashow the diversity of the event, although qualitatively similar. It could be due to theenvironmental effects. In the nearby universe, SNIa in early hosts show narrowerlightcurves than late-type hosts (Hamuy, 2000). But after lightcurve shape correc-tion, the dispersion is below observational errors. Similar results were just recentlyanalyzed at high redshift using Hubble Space Telescope imaging for morphologystudies, and Keck spectroscopy (Sullivan et al., 2003). After lightcurve shape andhost galaxy corrections, no deviation from a dark energy dominated universe werefound, but the Hubble diagram showed more scatter for the SNIa found in latetype hosts. We could take an empirical approach and only select sub-sample ofSNIa, for example only in elliptical galaxies, to reduce intrinsic dispersion. Amore ideal method, is to use a good theoretical modeling of spectra reproducingall SNIa events and instrumental transmission of each band properly calibrated toreproduce lightcurves at any redshift. SNIa spectrum models have unfortunatelynot yet reached the required precision and practicality for such an evolution-freemethod to work efficiently with only few parameters.

Two directions have been taken by the observational teams to see on a first order
if evolution has its role in the dimming of high redshift supernovae: going at higherredshift to see a departure on Hubble diagram, and increasing the statistical samplewith multi-band photometry and spectroscopy.

*K-Corrections and others*High redshift SNIa spectra are shifted toward longer wavelengths, and when integ-rated through the instrumental transmission, K-corrections are needed to recoverrest-frame photometry. In order to minimize the error made in extrapolating out-side the spectral range, we apply cross-band K-corrections, where we comparethe matching nearby SNIa bands with the high redshift ones (Kim, Goobar andPerlmutter, 1996). Nevertheless accuracies on various parameters affect the cor-rection. First, in order to perform the K-correction at any epoch of the super-nova, we need a template spectrum, not yet available with required accuracy atall wavelength. Late investigation showed that correlations between stretch, ex-tinction and K-corrections could correct a bit for a lack of template knowledge(Nugent, Kim and Perlmutter, 2002). Other inaccuracies come from calibrations toa standard band-pass system and calibration of supernovae spectra. A good cureto K-corrections will be when we have a large sample of well observed SNIaspectro-photometrically, such as the Nearby Supernova Factory project is aboutto produce.

Other sources of systematics are shown to be unsignificant, although poten-
tially problematic. Selection biases (such as Malmquist bias) are corrected throughmonte-carlo studies, but have not been quantified for the used low-redshift sample.

Gravitational lensing should affect

*z > *1 supernovae, but has been quantified to beless than 0

*.*02 mag for the published sample at ¯

*z *∼ 0

*.*5.

*More recent analyzes*Since the 1998 announcements of the two teams, there has been some progress,observing more supernovae at both nearby and high redshift. One of the achieveddevelopment was to get the Hubble diagram against the host galaxy morphology(Sullivan et al., 2003). High resolution images from HST and spectra from Keckwere used to a more detailed check on host galaxy effects on the set presen-ted in Perlmutter et al. (1999). No significant dimming due to extinction was re-vealed. Also preliminary results from 11 high-redshift SNIa more accurately photo-metered with HST (Knop et al., 2002) as well as other results from Krisciunas etal. (2003) converge to similar cosmological conclusions as the 1998 results.

**3. Prospects**
3.1. THE IMPORTANCE OF A NEARBY SUPERNOVA PROGRAM
A better understanding of intrinsic properties of SNIa is of primary importanceboth in a search for systematic effects and in the precise measurements of cosmo-logical parameters. Such an understanding could arise from precise spectroscopicobservations, achievable at low redshift. The

*Nearby Supernova Factory *1 is a pro-
PROBING DARK ENERGY WITH SUPERNOVA SEARCHES
ject to start in the year to come to detect and follow more than 400 supernovae at aredshift

*z < *0

*.*05. Thanks to a dedicated integral field spectrograph, it would allowto produce data-hyper-cubes

*(x, y, t, λ) *of a supernova and its local surroundings.

The wavelength coverage [0

*.*32

*, *1]

*µm *and high resolution 0.3

*nm *of a 6 × 6 fieldaround the target will allow us to directly point some problems addressed in theprevious paragraph: comparison with theoretical models, K-corrections, evolutionand extinction.

3.2. TOWARD THE NATURE OF DARK ENERGY: ONE STEP FURTHER
Going further into precision supernova cosmology will not only require betterknowledge of the supernova event, but also a larger homogeneous statistical sampleof high redshift supernovae. One of the main problems associated with high redshiftsupernova campaigns is managing, reduce and inter-calibrate all observations fromthe various telescopes used for follow-up photometry. Apart from regular searchesorganized every semester by the SCP and High-Z Team, two completely dedicatedproject aim to observe few hundreds supernovae at redshift between 0

*.*1

*< z < *0

*.*9:the SuperNova Legacy Survey (SNLS) 2 and the Essence project 3.

The SNLS is one of the CFHT Legacy Survey that will start February 2003. It
uses the Megaprime imager, a wide-field camera (Megacam) mounted on the primefocus of the CFHT-3.6m telescope in Hawaii. The camera is a mosaic of 36 thinned2K×4.5K CCDs covering one square degree. Four fields will be continuously ob-served for the next 5 years, in four bands (

*g, r, i, z*). The observation strategy hasthus been adapted, now allowing early discovery and well-sampled homogeneousfollow-up photometry of 600 SNIa in 5 years. Such a tremendous data set offer thepossibility of checking the standardization technique at various redshifts, and ondifferent filters.

bine the SNLS measurements with the Nearby Supernova Factory ones. Togetherwith a prior on
m from the CMB and the CFHT weak lensing survey, should lead
to an uncertainty on

*w*x of

*σ *∼ 0

*.*1.

3.3. UNAMBIGUOUSLY UNVEILING THE DARK ENERGY
Going at higher redshift and beating 2% measurements of cosmological parameterswill require a very large survey for well measured high redshift SNIa. Only spaceobservations can give us good photometric precision and spectroscopy at highredshift, where most of the SNIa flux is in infrared. The

*SuperNova AccelerationProbe *(SNAP) 4 is a project of a 2-m telescope in space, mounted with a widefield imager, an infrared imager and an integral field spectrometer. The observation
2 see http://snls.in2p3.fr3 see http://www.ctio.noao.edu/wproject4 see http://snap.lbl.gov

*Figure 4. *Expected Hubble diagram after 5 years of SNLS survey.

*Figure 5. *Expected confidence contours (68%) in the

*(w*0

*, w*1

*) *plane for the SNAP experiment whenthe Nearby Supernova Factory SNIa are added (in red-dashed) and when they are not. A flat universehas been assumed with a Gaussian prior on
strategy is similar to the SNLS, but covering 15 square degrees and reaching 2000well followed SNIa/year, with an expected photometric precision of less than 2%.

SNAP data quality should be able to discriminate among dark energy models
and alternative explanations to the acceleration of universe expansion. In principle,it would be able to detect time variation of the equation of state, together with priorinformation on
m and low-redshift SNIa from the Nearby Supernova Factory.

The SNAP design is still evolving. Depending on the availability of the funds,
SNAP is expected to be launched in 2010 and its mission should last at least forthree years. It is also designed to do a whole range of science, from galaxy structureto weak lensing.

PROBING DARK ENERGY WITH SUPERNOVA SEARCHES

**4. Conclusion**
Dark energy as a solution of dimming of type Ia supernovae at high redshift isalmost a secure fact, but as always, it needs further studies. Current constraints onthe nature of dark energy from SNIa can be greatly improved with a much bettercontrol of systematics, requiring precise nearby supernova observations, and byincreasing the sample of large high redshift supernovae. Few projects directly aimat building such samples. If type Ia supernovae keep holding their wonderful stand-ardization properties, we can expect within five years to have a first measurementthe dark energy equation of state with a precision of about 10%.

**Acknowledgments**
S. Fabbro thanks the support for this work provided by the Fundação para a Ciên-cia e Tecnologia through project PESO/P/PRO/15139/99 and a Fellowship grantthrough Project ESO/FNU/43749/2001.

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Source: http://thomasrauscher.ch/pubs/snIa_cosmology.pdf

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De communi mathematica scientia xxvii What the truly educated person should demand from the mathematician, and how he should judge his theory, and from what criteria he should comprehend its correctness But since it is the function of the educated man to be able to judge to a good approximation what is right or wrong in the contributions of the speaker, and we believe the ge