Ana Pelinson

Studying the decay of the vacuum energy with the observed density fluctuation spectrum

We investigate here models that suggest that the vacuum energy decays into cold dark matter (CDM) and show that the density fluctuation spectrum obtained from the cosmic microwave background (CMB) data together with large galaxy surveys (e.g., the Sloan Digital Sky Survey), puts strong limits on the rate of decay of the vacuum energy. CDM produced by a decaying vacuum energy would dilute the density fluctuation spectrum, created in the primordial universe and observed with large galaxy surveys at low redshifts. Our results indicate that the decay rate of the vacuum energy into CDM is extremely small.

Decay of the vacuum energy into cosmic microwave background photons

We examine the possibility of the decay of the vacuum energy into cosmic microwave background (CMB) photons. It is shown that observations of the primordial density fluctuation spectrum put strong limits on the possible decay rate. When photon creation due to the vacuum energy decay takes place, the standard linear temperature dependence, T(z)=T_0(1+z), where T_0 is the present CMB temperature, is modified. The decay is described by a generic temperature dependence, T(z)=T_0(1+z)^{1-\beta}, of the CMB photons. A strong limit on the maximum value of the decay rate is obtained by placing a maximum value on the \beta parameter: \beta_{max}\approx 3\times 10^{-3}.

Inflation without inflatons

(abridged)We present a model which predicts inflation without the presence of inflaton fields, based on the \epsilon R^2 and Starobinsky models. It links the above models to the observable universe, in particular, to the ratio r of tensor to scalar fluctuations. In our model, we assume the existence of particles with the mass M that have a long decay time. These particles which were gravitationally produced \sim 60e-folds before the end of inflation produced the nearly scale invariant scalar density fluctuations which are observed. Gravitational waves (tensor fluctuations) were also produced at this epoch. The ratio of tensor to scalar fluctuations r (which are to be measured in the near future to good accuracy) determines M, which together with H_0, determine the time at the end of inflation, t_end. At t_end, the Hubble parameter begins to oscillate rapidly, gravitationally producing the bulk of the M particles, which we identify with the matter content of the universe today. The time required for the universe to dissipate its vacuum energy into M particles is found to be t_dis \simeq 6M_Pl^2/M^3. We assume that the time t_RH, (called the reheating time) needed for the M particles to decay into relativistic particles, is very much greater than that necessary to create the M particles, t_dis. From the ratio f\equiv t_dis/t_RH and g_\ast (the total number of degrees of freedom of the relativistic particles) we can, then, evaluate the maximum temperature of the universe, T_max, and the reheat temperature, T_RH, at t_RH. Our model, thus, predicts M, t_dis, t_end, T_max, T_RH, t_max, and t_RH as a function of r, f, and g_\ast (and to a weaker extent the particle content of the vacuum near the Planck epoch).

Strong limits on the possible decay of the vacuum energy into CDM or CMB photons

We investigate models that suggest that the vacuum energy could decay into cold dark matter (CDM) or into a homogeneous distribution of thermalized cosmic microwave background (CMB) photons. We show that the agreement of the density fluctuation spectra obtained from the CMB and galaxy distribution data puts strong limits on the rate of vacuum energy decay. A vacuum energy decaying into CDM increases the density of the CDM ρ, diluting the CDM density fluctuations (δρ=ρ) 2 . The temperature fluctuations of the CMB photons (δT=T) 2 are approximately proportional to (δρ=ρ) 2 , at the recombination epoch. We define F as the predicted increase of (δρ=ρ) 2 (or (δT=T) 2 ) at the recombination epoch. Since the present observed (δρ=ρ) 2 derived from the CMB and galaxy distribution data agree to » 10%, the maximum value for F is Fmax » 1:1. Our results indicate that the rate of decay of the vacuum energy into CDM or CMB photons is extremely small.

Revisiting the modified Starobinsky model with cosmological constant

The Starobinsky model is a natural inflationary scenario in which inflation arises due to quantum effects of the massless matter fields. A modified version of the Starobinsky (MSt) model takes the masses of matter fields and the cosmological constant, Λ, into account. The equations of motion become much more complicated; however, approximate analytic and numeric solutions are possible. In the MSt model, inflation starts due to the supersymmetric (SUSY) particle content of the underlying theory, and the transition to the radiation-dominated epoch occurs due to the relatively heavy s-particles decoupling. For Λ = 0 the inflationary solution is stable until the last stage, just before decoupling. In the present paper we generalize this result for Λ ≠ 0, since Λ should be nonvanishing at the SUSY scale. We also take into account the radiative corrections to Λ. The main result is that the inflationary solution of the MSt model remains robust and stable.

WHAT IS THE SUSY MASS SCALE

The energy, or mass scale MSUSY, of the supersymmetry (SUSY) phase transition is, as yet, unknown. If it is very high (i.e. ≫103GeV), terrestrial accelerators will not be able to measure it. We determine MSUSY here by combining theory with the cosmic microwave background (CMB) data. Starobinsky suggested an inflationary cosmological scenario in which inflation is driven by quantum corrections to the vacuum Einsteins equation. The modified Starobinsky model (MSM) is a natural extension of this. In the MSM, the quantum corrections are the quantum fluctuations of the supersymmetric (SUSY) particles, whose particle content creates inflation and whose masses terminate it. Since the MSM is difficult to solve until the end of the inflation period, we assume here that an effective inflaton potential (EIP) that reproduces the time dependence of the cosmological scale factor of the MSM can be used to make predictions for the MSM. We predict the SUSY mass scale to be MSUSY ≃ 1015GeV, thus satisfying the requirement that the predicted density fluctuations of the MSM is in agreement with the observed CMB data.

A new inflaton model beginning near the planck epoch

The Starobinsky model predicts a primordial inflation period without the presence of an inflaton field. The modified version of this model predicts a simple time dependence for the Hubble parameter H(t), which decreases slowly between the Planck epoch and the end of the inflation, H(t) = MPl -bM2Plt, where b is a dimensionless constant to be adjusted from observations. We investigate an inflaton model which has the same time dependence for H(t). A reverse engineered inflaton potential for the time dependence of H is derived. Normalization of the derived inflaton potential is determined by the condition that the observed density fluctuations, dr/r » 10-5, are created at ~ 60 e-folds before the end of inflation. The derived potential indicates an energy (mass) scale, Mend ~ 1013 GeV, at the end of inflation. Using the slow roll parameters, which are obtained from this potential, we calculate the spectral index for the scalar modes nS and the relative amplitude of the tensor to scalar modes r. A tensor contribution, r ~ 0.13, and an approximately Harrison-Zeldovich density perturbation spectrum, nS ~ 0.95, are predicted.