Recent CMB Observations and the Ionization History of the Universe

Interest in non-standard recombination scenarios has been spurred by recent cosmic microwave background (CMB) results from BOOMERANG and MAXIMA, which show an unexpectedly low second acoustic peak, resulting in a best-fit baryon density that is 50% larger than the prediction of big-bang nucleosynthesis (BBN). This apparent discrepancy can be avoided if the universe has a non-standard ionization history in which the recombination of hydrogen is significantly delayed relative to the standard model. While future CMB observations may eliminate this discrepancy, it is useful to develop a general framework for analyzing non-standard ionization histories. We develop such a framework, examining non-standard models in which the hydrogen binding energy E_b and the overall expression for the time rate of change of the ionized fraction of electrons are multiplied by arbitrary factors. This set of models includes a number of previously-proposed models as special cases. We find a wide range of models with delayed recombination that are able to fit the CMB data with a baryon density in accordance with BBN, but there are even allowed models with earlier recombination than in the standard model. A generic prediction of these models is that the third acoustic CMB peak should be very low relative to what is found in the standard model. This is the case even for the models with earlier recombination than in the standard model, because here the third peak is lowered by an increased diffusion damping at recombination relative to the standard model. Interestingly, the specific height of the third peak depends sensitively on the model parameters, so that future CMB measurements will be able to distinguish between different non-standard recombination scenarios.Comment: 10 pages, 9 figs, uses RevTex, version to appear in PR

Oscillating and Static Universes from a Single Barotropic Fluid

We consider cosmological solutions to general relativity with a single barotropic fluid, where the pressure is a general function of the density, $p = f(\rho)$. We derive conditions for static and oscillating solutions and provide examples, extending earlier work to these simpler and more general single-fluid cosmologies. Generically we expect such solutions to suffer from instabilities, through effects such as quantum fluctuations or tunneling to zero size. We also find a classical instability ("no-go" theorem) for oscillating solutions of a single barotropic perfect fluid due to a necessarily negative squared sound speed.Comment: 5 pages; v2: additional references, minor clarification in Sec. IIC, matches version published in JCA

Big Bang nucleosynthesis with a stiff fluid

Models that lead to a cosmological stiff fluid component, with a density $\rho_S$ that scales as $a^{-6}$, where $a$ is the scale factor, have been proposed recently in a variety of contexts. We calculate numerically the effect of such a stiff fluid on the primordial element abundances. Because the stiff fluid energy density decreases with the scale factor more rapidly than radiation, it produces a relatively larger change in the primordial helium-4 abundance than in the other element abundances, relative to the changes produced by an additional radiation component. We show that the helium-4 abundance varies linearly with the density of the stiff fluid at a fixed fiducial temperature. Taking $\rho_{S10}$ and $\rho_{R10}$ to be the stiff fluid energy density and the standard density in relativistic particles, respectively, at $T = 10$ MeV, we find that the change in the primordial helium abundance is well-fit by $\Delta Y_p = 0.00024(\rho_{S10}/\rho_{R10})$. The changes in the helium-4 abundance produced by additional radiation or by a stiff fluid are identical when these two components have equal density at a "pivot temperature", $T_*$, where we find $T_* = 0.55$ MeV. Current estimates of the primordial $^4$He abundance give the constraint on a stiff fluid energy density of $\rho_{S10}/\rho_{R10} < 30$.Comment: 6 pages, 2 figures. Clarification added: element abundances derived using a full numerical calculation. Version accepted at PR

Decaying dark matter mimicking time-varying dark energy

A $\Lambda$CDM model with dark matter that decays into inert relativistic energy on a timescale longer than the Hubble time will produce an expansion history that can be misinterpreted as stable dark matter with time-varying dark energy. We calculate the corresponding spurious equation of state parameter, $\widetilde w_\phi$, as a function of redshift, and show that the evolution of $\widetilde w_\phi$ depends strongly on the assumed value of the dark matter density, erroneously taken to scale as $a^{-3}$. Depending on the latter, one can obtain models that mimic quintessence ($\widetilde w_\phi > -1$), phantom models ($\widetilde w_\phi < -1$) or models in which the equation of state parameter crosses the phantom divide, evolving from $\widetilde w_\phi > -1$ at high redshift to $\widetilde w_\phi < -1$ at low redshift. All of these models generically converge toward $\widetilde w_\phi \approx -1$ at the present. The degeneracy between the $\Lambda$CDM model with decaying dark matter and the corresponding spurious quintessence model is broken by the growth of density perturbations.Comment: 6 pages, 2 figures. Added discussion of linear perturbation growth - version accepted at PR

Dark energy with w→−1w \rightarrow -1: Asymptotic Λ\Lambda versus pseudo-Λ\Lambda

If the dark energy density asymptotically approaches a nonzero constant, $\rho_{DE} \rightarrow \rho_0$, then its equation of state parameter $w$ necessarily approaches $-1$. The converse is not true; dark energy with $w \rightarrow -1$ can correspond to either $\rho_{DE} \rightarrow \rho_0$ or $\rho_{DE} \rightarrow 0$. This provides a natural division of models with $w \rightarrow -1$ into two distinct classes: asymptotic $\Lambda$ ($\rho_{DE} \rightarrow \rho_0$) and pseudo-$\Lambda$ ($\rho_{DE} \rightarrow 0$). We delineate the boundary between these two classes of models in terms of the behavior of $w(a)$, $\rho_{DE}(a)$, and $a(t)$. We examine barotropic and quintessence realizations of both types of models. Barotropic models with positive squared sound speed and $w \rightarrow -1$ are always asymptotically $\Lambda$; they can never produce pseudo-$\Lambda$ behavior. Quintessence models can correspond to either asymptotic $\Lambda$ or pseudo-$\Lambda$ evolution, but the latter is impossible when the expansion is dominated by a background barotropic fluid. We show that the distinction between asymptotic $\Lambda$ and pseudo-$\Lambda$ models for $w> -1$ is mathematically dual to the distinction between pseudo-rip and big/little rip models when $w < -1$.Comment: 7 pages, no figures, references adde