Cosmology and Fundamental Physics with the Euclid Satellite

Measuring the speed of light with baryon acoustic oscillations

In this Letter, we describe a new method to use baryon acoustic oscillations (BAO) to derive a constraint on the possible variation of the speed of light. The method relies on the fact that there is a simple relation between the angular diameter distance (D(A)) maximum and the Hubble function (H) evaluated at the same maximum-condition redshift, which includes speed of light c. We note the close analogy of the BAO probe with a laboratory experiment: here we have D(A) which plays the role of a standard (cosmological) ruler, and H^{-1}, with the dimension of time, as a (cosmological) clock. We evaluate if current or future missions such as Euclid can be sensitive enough to detect any variation of c.

Reheating constraints to inflationary models

Evidence from the BICEP2 experiment for a significant gravitational-wave background has focused attention on inflaton potentials V(ϕ)∝ϕ(α) with α = 2 ("chaotic" or "m(2)ϕ(2)" inflation) or with smaller values of α, as may arise in axion-monodromy models. Here we show that reheating considerations may provide additional constraints to these models. The reheating phase preceding the radiation era is modeled by an effective equation-of-state parameter w(re). The canonical reheating scenario is then described by w(re) = 0. The simplest α = 2 models are consistent with w(re) = 0 for values of n(s) well within the current 1σ range. Models with α = 1 or α = 2/3 require a more exotic reheating phase, with -1/3 < w(re) < 0, unless n(s) falls above the current 1σ range. Likewise, models with α = 4 require a physically implausible w(re) > 1/3, unless n(s) is close to the lower limit of the 2σ range. For m(2)ϕ(2) inflation and canonical reheating as a benchmark, we derive a relation log(10)(T(re)/10(6) GeV) ≃ 2000(n(s)-0.96) between the reheat temperature T(re) and the scalar spectral index n(s). Thus, if n(s) is close to its central value, then T(re) ≲ 10(6) GeV, just above the electroweak scale. If the reheat temperature is higher, as many theorists may prefer, then the scalar spectral index should be closer to n(s) ≃ 0.965 (at the pivot scale k = 0.05 Mpc(-1)), near the upper limit of the 1σ error range. Improved precision in the measurement of n(s) should allow m(2)ϕ(2), axion monodromy, and ϕ(40) models to be distinguished, even without precise measurement of r, and to test the m(2)ϕ(2) expectation of n(s) ≃ 0.965.

ϕ(2) or not ϕ(2): testing the simplest inflationary potential

The simplest inflationary model V=1/2m(2)ϕ(2) represents the benchmark for future constraints. For a quadratic potential, the quantity (n(s)-1)+r/4+11(n(s)-1)(2)/24 vanishes (up to corrections which are cubic in slow roll) and can be used to parametrize small deviations from the minimal scenario. Future constraints on this quantity will be able to distinguish a quadratic potential from a pseudo-Nambu-Goldstone boson with f≲30M(pl) and set limits on the deviation from unity of the speed of sound |c(s)-1|≲3×10(-2) (corresponding to an energy scale Λ≳2×10(16)  GeV) and on the contribution of a second field to perturbations (≲6×10(-2)). The limiting factor for these bounds will be the uncertainty on the spectral index. The error on the number of e-folds will be ΔN≃0.4, corresponding to an error on the reheating temperature ΔT(rh)/T(rh)≃1.2. We comment on the relevance of non-Gaussianity after BICEP2 results.

Topology and dark energy: testing gravity in voids

Modified gravity has garnered interest as a backstop against dark matter and dark energy (DE). As one possible modification, the graviton can become massive, which introduces a new scalar field--here with a Galileon-type symmetry. The field can lead to a nontrivial equation of state of DE which is density and scale dependent. Tension between type Ia supernovae and Planck could be reduced. In voids, the scalar field dramatically alters the equation of state of DE, induces a soon-observable gravitational slip between the two metric potentials, and develops a topological defect (domain wall) due to a nontrivial vacuum structure for the field.