Eddington-Born-Infeld gravity and the large scale structure of the Universe

It has been argued that a Universe governed by Eddington-Born-Infeld gravity can be compatible with current cosmological constraints. The extra fields introduced in this theory can behave as both dark matter and dark energy, unifying the dark sector in one coherent framework. We show the various roles the extra fields can play in the expansion of the Universe and study the evolution of linear perturbations in the various regimes. We find that, as a unified theory of the dark sector, Eddington-Born-Infeld gravity will lead to excessive fluctuations in the cosmic microwave background on large scales. In the presence of a cosmological constant, however, the extra fields can behave as a form of nonparticulate dark matter and can lead to a cosmology which is entirely compatible with current observations of large scale structure. We discuss the interpretation of this form of dark matter and how it can differ from standard, particulate dark matter.

Figure 1

Upper panel: The locus of fixed ${\tau }_0$ and angular diameter distance to recombination, by varying ${\omega }_L$ and $w_0$ keeping all other parameters fixed. The value ${\omega }_{\Lambda }=0.36$ corresponds to the WMAP5 best-fit model. The other EBI parameters are $1-\alpha ={10}^{-6}$ and $\ell ={10}^9\mathrm{Mpc}$. Lower panel: A similar locus curve, only now we vary $\alpha$ and $w_0$ keeping all other parameters fixed and in particular ${\omega }_{\Lambda }=0$. The alphabetical labels are explained and discussed in the main text.

Figure 2

Four models from the locus curve of Fig. 1 $({\omega }_{\Lambda },w_0)=(0.36,6\times {10}^{-8})$ (upper left), $(0.2,0.43)$ (upper right), $(0.1,0.65)$ (lower left), and $(0,0.84)$ (lower right). The curves are EBI (solid line), $\Lambda$ (dashed line), baryons (dotted line) and radiation (long-dashed line). Note that in the last case (lower right), the final state of the EBI field is an approximate cosmological constant. The actual phase is the constant-$w$ phase with $w$ being extremely close to $-1$ due to $1-\alpha ={10}^{-6}$.

Figure 3

The same four models as Fig. 2. They are from the locus curve of Fig. 1 $({\omega }_{\Lambda },w_0)=(0.36,6\times {10}^{-8})$ (upper left), $(0.2,0.43)$ (upper right), $(0.1,0.65)$ (lower left), and $(0,0.84)$ (lower right). The curves are $X$ (solid line), $Y$ (dashed line), $\frac{\dot{X}}{X}$(dotted line) and $\frac{\dot{Y}}{Y}$ (long-dashed line).

Figure 4

The cosmic microwave background angular power spectrum $C_{\ell }$ for the models described in the realistic background evolution. The solid curve is model A (the $\Lambda \mathrm{EBI}$ model) which is indistinguishable from the best-fit WMAP5 $\Lambda \mathrm{CDM}$ model. The long-dashed curve is model B, the short-dashed curve is model C, the dotted-dashed curve is model D and the dotted curve is model E. All models have the same initial amplitude, tilt (0.962) and nonzero optical depth to reionization (0.088) as the best-fit WMAP5 model.

Figure 5

The Newtonian potential combination $\Phi +\Psi$ which is relevant to the integrated Sachs-Wolfe effect for the same set of models A–E, plotted against $\tau /{\tau }_0$, where ${\tau }_0$ is the conformal time today. In the upper panel we display model A (solid curve), model B (long-dashed curve) and model C (short-dashed curve). In the lower panel we show again model C (short-dashed curve) to be compared with model D (dotted-dashed curve) and model E (dotted curve). Notice that $\Phi +\Psi$ for models B–E oscillates during the transition to de Sitter phase (which is usually a constant-$w$ phase), while models C–E also start to diverse during the de Sitter phase. The presence of a bare cosmological constant in model B seems to curb the divergence, although the oscillation remains.

Figure 6

The baryon power spectrum $P(k)$ for the same set of models A–E. Once again we show model A (solid curve) which is indistinguishable from the best-fit WMAP5 $\Lambda \mathrm{CDM}$ model. The long-dashed curve is model B, the short-dashed curve is model C, the dotted-dashed curve is model D and the dotted curve is model E. All models have the same tilt (0.962) as the best-fit WMAP5 model.

Figure 7

The cosmic microwave background angular power spectrum $C_{\ell }$ (upper panel) with WMAP5 data and baryon power spectrum $P(k)$ (lower panel) for the $\Lambda \mathrm{EBI}$ model with SDSS data (model A). Both spectra are indistinguishable from the best-fit WMAP5 $\Lambda \mathrm{CDM}$ model.

Figure 8

The Newtonian potential combination $\Phi -\Psi$ for the same set of models A–E, plotted against $\tau /{\tau }_0$, where ${\tau }_0$ is the conformal time today. In the upper panel we display model A (solid curve), model B (long-dashed curve) and model C (short-dashed curve). In the lower panel we show again model C (short-dashed curve) to be compared with model D (dotted-dashed curve) and model E (dotted curve). Notice that $\Phi -\Psi$ for models B–E oscillates during the transition to de Sitter phase (which is usually a constant-$w$ phase), while models C–E also start to diverse during the de Sitter phase. The presence of a bare cosmological constant in model B seems to curb the divergence, although the oscillation remains.