Warped compactification to de Sitter space

We explore in detail the prospects of obtaining a four-dimensional de Sitter universe in classical supergravity models with warped and time-independent extra dimensions, presenting explicit cosmological solutions of the $(4+n)$-dimensional Einstein equations with and without a bulk cosmological constant term. For the first time in the literature we show that there may exist a large class of warped supergravity models with a noncompact extra dimension which lead to a finite 4D Newton constant as well as a massless 4D graviton localised on an inflating four-dimensional FLRW universe. This result helps establish that the `no-go' theorem forbidding acceleration in `standard' compactification of string/M-theory on physically compact spaces should not apply to a general class of warped supergravity models that allows at least one noncompact direction. We present solutions for which the size of the radial dimension takes a constant value in the large volume limit, providing an explicit example of spontaneous compactification.Comment: 19 pages, 2 figures; final (journal) versio

Accelerating cosmologies from compactification with a twist

It is demonstrated by explicit solutions of the (4+n)-dimensional vacuum Einstein equations that accelerating cosmologies in the Einstein conformal frame can be obtained by a time-dependent compactification of string/M-theory, even in the case that internal dimensions are Ricci-flat, provided one includes one or more geometric twists. Such acceleration is transient. When both compact hyperbolic internal spaces and geometric twists are included, however, the period of accelerated expansion may be made arbitrarily large.Comment: 5 pages, 1 figure, RevTeX

Gauss-Bonnet assisted braneworld inflation in light of BICEP2 and Planck data

Motivated by the idea that quantum gravity corrections usually suppress the power of the scalar primordial spectrum (E-mode) more than the power of the tensor primordial spectrum (B-mode), in this paper we construct a concrete gravitational theory in five-dimensions for which $V(\phi)\propto \phi^n$-type inflation ($n\ge 1$) generates an appropriate tensor-to-scalar ratio that may be compatible with the BICEP2 and Planck data together. The true nature of gravity is five-dimensional and described by the action $S = \int d^5{x} \sqrt{|g|} M^3 (- 6\lambda M^2 + R + \alpha M^{-2} {\cal R}^2)$ where $M$ is the five-dimensional Planck mass and ${\cal R}^2=R^2-4 R_{ab} R^{ab} + R_{abcd} R^{abcd}$ is the Gauss-Bonnet (GB) term. The five-dimensional "bulk" spacetime is anti-de Sitter ($\lambda<0$) for which inflation ends naturally. The effects of ${\cal R}^2$ term on the magnitudes of scalar and tensor fluctuations and spectral indices are shown to be important at the energy scale of inflation. For GB-assisted $m^2\phi^2$-inflation, inflationary constraints from BICEP2 and Planck, such as, $n_s\simeq 0.9603 (\pm 0.0073)$, $r=0.16 (+0.06-0.05)$ and $V_*^{1/4} \sim 1.5\times 10^{16} {\text GeV}$ are all satisfied for $(-\lambda \alpha) \simeq (3-300)\times 10^{-5}$.Comment: 5 pages, 4 figures, revtex4; v2: some additions to text in response to comments, published versio

Natural Braneworld Inflation in Light of Recent Results from Planck and BICEP2

In this paper we report on a major theoretical observation in cosmology. We present a concrete cosmological model for which inflation has natural beginning and natural ending. Inflation is driven by a cosine-form potential, $V(\phi)= \Lambda^4 (1-\cos(\phi/f))$, which begins at $\phi \lesssim \pi f$ and ends at $\phi =\phi_{\text{end}} \lesssim 5 f/3$. The distance traversed by the inflaton field $\phi$ is sub-Planckian. The Gauss-Bonnet term ${\cal R}^2$ arising as leading curvature corrections in the action $S = \int d^5{x} \sqrt{-g_{5}} M^3 (- 6\lambda M^2 + R + \alpha M^{-2} {\cal R}^2)+ \int d^{4}x \sqrt{-g_{4}} (\dot{\phi}^2/2 - V(\phi)- \sigma +{\cal L}_{\text{matter}})$ (where $\alpha$ and $\lambda$ are constants and $M$ is the five-dimensional Planck mass) plays a key role to terminate inflation. The model generates appropriate tensor-to-scalar ratio $r$ and inflationary perturbations that are consistent with results from Planck and BICEP2. For example, for $N_*= 50-60$ and $n_s\sim 0.960\pm 0.005$, the model predicts that $M\sim 5.64\times 10^{16}\,{\text{GeV}}$ and $r\sim (0.14-0.21)$ [$N_*$ is the number of {\it e}--folds of inflation and $n_s$ ($n_{t}$) is the scalar (tensor) spectrum spectral index]. The ratio $-n_t/r$ is (13% -- 24%) less than its value in 4D Einstein gravity, $-n_t/r=1/8$. The upper bound on the energy scale of inflation $V^{1/4}=2.37\times 10^{16}\,{\text{GeV}}$ ($r<0.27$) implies that $(-\lambda \alpha) \gtrsim 75 \times 10^{-5}$ and $\Lambda<2.17\times 10^{16}\,{\text{GeV}}$, which thereby rule out the case $\alpha=0$ (Randall-Sundrum model). The true nature of gravity is holographic as implied by braneworld realization of string and M theory. The model correctly predicts a late epoch cosmic acceleration with the dark energy equation of state ${\text w}_{\text{DE}}\approx -1$.Comment: 13 pages, 14 figures; v2: minor changes, published versio

Extra dimensions, warped compactifications and cosmic acceleration

We report on explicit cosmological solutions within the framework of an inflating de Sitter brane embedded in five- and ten-dimensional bulk spacetimes. In the specific example we study the brane tension is induced by the curvature related to the expansion of a physical 3+1 spacetime rather than by a bulk cosmological term. In a generic situation with nonzero brane tension, the expansion of the universe accelerates eventually. We also show that inflationary cosmology is possible for a wide class of metrics without violating four- and higher-dimensional null energy condition.Comment: 10 pages; major addition, references added, matches published versio