We discuss the gravitational wave background generated by primordial density perturbations evolving during the radiation era. At second-order in a perturbative expansion, density fluctuations produce gravitational waves. We calculate the power spectra of gravitational waves from this mechanism, and show that, in principle, future gravitational wave detectors could be used to constrain the primordial power spectrum on scales vastly different from those currently being probed by large-scale structure. As examples we compute the gravitational wave background generated by both a power-law spectrum on all scales, and a delta-function power spectrum on a single scale.

We investigate the general relativistic dynamics of Robertson-Walker models with a non-linear equation of state (EoS), focusing on the quadratic case P = P0 + αρ + βρ 2 . This may be taken to represent the Taylor expansion of any arbitrary barotropic EoS, P (ρ). With the right combination of P0, α and β, it serves as a simple phenomenological model for dark energy, or even unified dark matter. Indeed we show that this simple model for the EoS can produce a large variety of qualitatively different dynamical behaviors that we classify using dynamical systems theory. An almost universal feature is that accelerated expansion phases are mostly natural for these non-linear EoS's. These are often asymptotically de Sitter thanks to the appearance of an effective cosmological constant. Other interesting possibilities that arise from the quadratic EoS are closed models that can oscillate with no singularity, models that bounce between infinite contraction/expansion and models which evolve from a phantom phase, asymptotically approaching a de Sitter phase instead of evolving to a "Big Rip". In a second paper we investigate the effects of the quadratic EoS in inhomogeneous and anisotropic models, focusing in particular on singularities.PACS numbers: 98.80. Jk, 95.35.+d, 95.36.+x

We investigate the effect that the average backreaction of structure formation has on the dynamics of the cosmological expansion, within the concordance model. Our approach in the Poisson gauge is fully consistent up to second-order in a perturbative expansion about a flat Friedmann background, including a cosmological constant. We discuss the key length scales which are inherent in any averaging procedure of this kind. We identify an intrinsic homogeneity scale that arises from the averaging procedure, beyond which a residual offset remains in the expansion rate and deceleration parameter. In the case of the deceleration parameter, this can lead to a quite large increase in the value, and may therefore have important ramifications for dark energy measurements, even if the underlying nature of dark energy is a cosmological constant. We give the intrinsic variance that affects the value of the effective Hubble rate and deceleration parameter. These considerations serve to add extra intrinsic errors to our determination of the cosmological parameters, and, in particular, may render attempts to measure the Hubble constant to percent precision overly optimistic.

We investigate the spectrum of vector modes today which is generated at second order by density perturbations. The vector mode background that is generated by structure formation is small but in principle it contributes to the integrated Sachs-Wolfe effect, to redshift-space distortions and to weak lensing. We recover, clarify and extend previous results, and explain carefully why no vorticity is generated in the fluid at second order. The amplitude of the induced vector mode in the metric is around 1% that of the first-order scalars on small scales. We also calculate the power spectrum and the energy density of the vector part of the shear at second order.

While vector modes are usually ignored in cosmology since they are not produced during inflation they are inevitably produced from the interaction of density fluctuations of differing wavelengths. This effect may be calculated via a second-order perturbative expansion. We investigate this effect during the radiation era. We discuss the generation mechanism by investigating two scalar modes interacting, and we calculate the power of vector modes generated by a power-law spectrum of density perturbations on all scales.Comment: 10 pages, 2 figures, minor changes in main text and new appendix added to match the accepted version for Physical Review D publicatio