[Paper Review] Constraints on dark energy from the observed density fluctuations spectrum and supernova data

R. Opher, Ana Pelinson|arXiv (Cornell University)|May 23, 2005

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper constrains dark energy models using the observed density fluctuation spectrum and supernova data, showing that the vacuum metamorphosis model (VMM) and brane-world model (BWM) are excluded when combined with the observed matter density $Ω_M^0 = 0.28 \pm 0.02$ and $F_{\text{max}} = 0.1$ for the discrepancy in $(\delta\rho/\rho)^2$ between CMB and galaxy data. It further restricts the parametrized dark energy equation of state to $-1.86 < w_0 < -1.72$ and $1.53 < w_a < 2.9$, and rejects the supergravity model with $w_0 = -0.82$, $w_a = 0.58$ due to a large $F \approx 0.38$. The results strongly constrain viable dark energy models beyond the cosmological constant.

ABSTRACT

One of the greatest challenges in cosmology today is to determine the nature of dark energy, the source of the observed present acceleration of the universe. High precision experiments are being developed to reduce the uncertainties in the observations. Recently, we showed that the agreement to an accuracy of 10% of measurements of the present density fluctuations (δρ/ρ)^2, derived from galaxy distribution (GD) data and cosmic microwave background (CMB) anisotropies in the \LambdaCDM model, puts very strong limits on the possible decay of the vacuum energy into cold dark matter. Using this agreement, combined with the evidence that the matter density Ω_M^0=0.28\pm 0.02 and that the universe is approximately flat, we show that the vacuum metamorphosis model (VMM) and the popular brane-world model (BWM), both used to explain dark energy, can be discarded. When we relax the Ω_M^0 requirement, we find that an agreement within 10% can be obtained only with Ω_M^0\simeq 0.36 for the VMM and Ω_M^0\simeq 0.73 for the BWM, both of which are not consistent with observations. The agreement of the CMB and GD data and previous constraints from SNIa data exclude, or put strong limits on, other dark energy models, which have been suggested, that can be described by the parametrized equation of state (EOS) w=p/ρ= w_0 + w_a(1-a), where w_0 and w_a are constants, a is the cosmological scale factor and p (ρ) is the pressure (energy density) of the dark energy. We find that the supergravity (SUGRA) model with w_0=-0.82 and w_a=0.58 can be discarded. In general, we find best values -1.86

Motivation & Objective

• To test the viability of the vacuum metamorphosis model (VMM) and brane-world model (BWM) as dark energy candidates using observational constraints.
• To constrain the parametrized dark energy equation of state $w(a) = w_0 + w_a(1-a)$ using supernova (SNIa) data and the observed $F = 0.1$ discrepancy in density fluctuations.
• To evaluate the supergravity (SUGRA) model with $w_0 = -0.82$, $w_a = 0.58$ against the same observational constraints.
• To determine whether these models can reproduce the observed $F \leq 0.1$ between CMB and galaxy distribution (GD) data for the density fluctuation spectrum.

Proposed method

• Numerical computation of the linear growth factor $G = (\delta\rho/\rho)/a$ for various dark energy models using the Friedmann equation with effective equation of state $w(z)$.
• Use of the parametrized equation of state $w(a) = w_0 + w_a(1-a)$ to describe dark energy, with $w_0$ and $w_a$ as free parameters.
• Comparison of the predicted $(\delta\rho/\rho)^2$ from CMB and galaxy distribution data to compute the discrepancy $F = |(\delta\rho/\rho)^2_{\text{CMB}} - (\delta\rho/\rho)^2_{\text{GD}}| / (\delta\rho/\rho)^2_{\text{CMB}}$.
• Application of constraints from the Gold SNIa dataset to restrict the allowed ranges of $w_0$ and $w_a$, while enforcing $F \leq 0.1$ and $\Omega_M^0 = 0.28 \pm 0.02$.
• Evaluation of the SUGRA model by computing its $F$ value and comparing it to the $F_{\text{max}} = 0.1$ threshold.
• Use of the flat universe assumption and the $\Lambda$CDM model as a benchmark for consistency checks.

Experimental results

Research questions

• RQ1 Can the vacuum metamorphosis model (VMM) be consistent with the observed $F \leq 0.1$ in density fluctuation measurements and $\Omega_M^0 = 0.28 \pm 0.02$?
• RQ2 Can the brane-world model (BWM) be viable given the same observational constraints on $F$ and $\Omega_M^0$?
• RQ3 What are the tightest allowed ranges for $w_0$ and $w_a$ in the parametrized dark energy model $w(a) = w_0 + w_a(1-a)$ when combining SNIa data and the $F \leq 0.1$ condition?
• RQ4 Is the supergravity (SUGRA) model with $w_0 = -0.82$, $w_a = 0.58$ compatible with the $F \leq 0.1$ and $\Omega_M^0 = 0.28 \pm 0.02$ constraints?
• RQ5 What matter density $\Omega_M^0$ is required for VMM and BWM to achieve $F \leq 0.1$, and is it consistent with observations?

Key findings

• The vacuum metamorphosis model (VMM) can only achieve $F \leq 0.1$ if $\Omega_M^0 \approx 0.36$, which is inconsistent with the observed $\Omega_M^0 = 0.28 \pm 0.02$, thus excluding the model.
• The brane-world model (BWM) requires $\Omega_M^0 \approx 0.72$ to achieve $F \leq 0.1$, a value significantly higher than the observed $\Omega_M^0 = 0.28 \pm 0.02$, thus excluding the model.
• For the parametrized dark energy model $w(a) = w_0 + w_a(1-a)$, the best-fit ranges are constrained to $-1.86 < w_0 < -1.72$ and $1.53 < w_a < 2.9$ when combining SNIa data and the $F \leq 0.1$ condition.
• The supergravity (SUGRA) model with $w_0 = -0.82$, $w_a = 0.58$ yields $F_{\text{SUGRA}} \approx 0.38_{+0.02}^{+0.04}$, which exceeds the $F_{\text{max}} = 0.1$ threshold, thus rejecting the model.
• For redshifts $z \sim 0.5-1$, where supernova data is most sensitive, the effective equation of state is $w \sim -1$ for the constrained $w_0$ and $w_a$ range.
• The study concludes that models with $w_0 > -1.86$ or $w_a < 1.53$ are inconsistent with the combined constraints from $F \leq 0.1$, $\Omega_M^0 = 0.28 \pm 0.02$, and SNIa data.