Flat FLRW Spacetime Research Articles

Creation of spin1/2particles and renormalization in FLRW spacetime

Within the framework of adiabatic regularization, we present a simple formalism to calculate number density and renormalized energy-momentum density of spin $1/2$ particles in spatially flat FLRW spacetimes using an appropriate WKB ansatz for the adiabatic expansion for the field modes. The conformal and axial anomalies thus found are in exact agreement with those obtained from other renormalization methods. This formalism can be considered as an appropriate extension of the techniques originally introduced for scalar fields, applicable to fermions in curved space.

Testing general relativity using the evolution of linear bias

We investigate the cosmic evolution of the linear bias in the framework of a flat FLRW spacetime. We consider metric perturbations in the Newtonian gauge, including Hubble scale effects. Making the following assumptions, (i) scale independent current epoch bias $b_0$, (ii) equal accelerations between tracers and matter, (iii) unimportant halo merging effects (which is quite accurate for $z<3$), we analytically derive the scale dependent bias evolution. The identified scale dependence is only due to Hubble scale evolution GR effects, while other scale dependence contributions are ignored. We find that up to galaxy cluster scales the fluctuations of the metric do not introduce a significant scale dependence in the linear bias. Our bias evolution model is then used to derive a connection between the matter growth index $\gamma$ and the observable value of the tracer power spectrum normalization $\sigma_8(z)$. We show how this connection can be used as an observational test of General Relativity on extragalactic scales.

Cosmological dynamics of fourth-order gravity: A compact view

We construct a compact phase space for flat FLRW spacetimes with standard matter described by a perfect fluid with a barotropic equation of state for general f(R) theories of gravity, subject to certain conditions on the function f. We then use this framework to study the behaviour of the phase space of Universes with a non-negative Ricci scalar in R + {\alpha}R^n gravity. We find a number of interesting cosmological evolutions which include the possibility of an initial unstable power-law inflationary point, followed by a curvature fluid dominated phase mimicking standard radiation, then passing through a standard matter (CDM) era and ultimately evolving asymptotically towards a de-Sitter-like late-time accelerated phase.

The horizon-entropy increase law for causal and quasi-local horizons and conformal field redefinitions

We explicitly prove the horizon-entropy increase law for both causal and quasi-locally defined horizons in scalar–tensor and f(R) gravity theories. Contrary to causal event horizons, future outer trapping horizons are not conformally invariant and we provide a modification of trapping horizons to complete the proof, using the idea of generalized entropy. This modification means that they are no longer foliated by marginally outer trapped surfaces but fixes the location of the horizon under a conformal transformation. We also discuss the behaviour of horizons in ‘veiled’ general relativity and show, using this new definition, how to locate cosmological horizons in flat Minkowski space with varying units, which is physically identified with a spatially flat FLRW spacetime.

THE COSMIC COINCIDENCE IN BRANS–DICKE COSMOLOGIES

Among the suggested solutions to the cosmological constant problem, we find the idea of a dynamic vacuum, with an energy density decaying with the universe expansion. We investigate the possibility of a variation in the gravitational constant as well, induced, at the cosmological scale, by the vacuum decay. We consider an effective Brans–Dicke theory in the spatially flat FLRW spacetime, finding late time solutions characterized by a constant ratio between the matter and vacuum energy densities. By using the observed limits for the universe age, we fix the only free parameter of our solutions, obtaining a relative matter density in the range 0.25&lt;Ωm&lt;0.4. In particular, for Ht = 1 we obtain Ωm= 1/3. This constitutes a possible explanation for another problem related to the cosmological term, the cosmic coincidence problem.

A NO-CHAOS THEOREM FOR NON-MINIMALLY COUPLED SCALAR FIELD COSMOLOGY AND A NEW COSMOGENESIS SCENARIO

A general dynamical system approach to classical self-consistent scalar field cosmology is presented in the framework of spatially flat FLRW space–times, for arbitrary potentials and arbitrary non-minimal coupling. We show that these universes cannot undergo chaotic behaviors, thus suggesting a possible new role of inflation in cosmology. An unexpectedly involved topology of the phase-portrait of the cosmological dynamics is exhibited: Dynamically forbidden regions, playing a crucial dynamical role, appear. A new exact critical solution, a heteroclinic orbit, connects two de Sitter inflationary regimes. We suggest a novel intriguing semiclassical cosmogenesis scenario in which the quantized scalar field could tunnel through the classically forbidden region, from the Minkowski space–time towards the nearest classically allowed solution: The critical one.

Explicit Analytic Solutions of Classical Scalar Field Cosmology

A class of explicit and exact solutions is obtained for the equations governingthe evolution of spatially flat FLRW spacetimes in interaction with a classicalmassive scalar field in the presence of conformal coupling and of a quarticself-interaction potential. These solutions only exist for nonvanishing cosmologicalconstant. The equation of state is calculated self-consistently.