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

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

Cosmology of a Friedmann-Lama\^itre-Robertson-Walker 3-brane, Late-Time Cosmic Acceleration, and the Cosmic Coincidence

A late epoch cosmic acceleration may be naturally entangled with cosmic coincidence -- the observation that at the onset of acceleration the vacuum energy density fraction nearly coincides with the matter density fraction. In this Letter we show that this is indeed the case with the cosmology of a Friedmann-Lama\^itre-Robertson-Walker (FLRW) 3-brane in a five-dimensional anti-de Sitter spacetime. We derive the four-dimensional effective action on a FLRW 3-brane, which helps define a general reduction formula, namely, $M_P^{2}=\rho_{b}/|\Lambda_5|$, where $M_{P}$ is the effective Planck mass, $\Lambda_5$ is the 5-dimensional cosmological constant, and $\rho_b$ is the sum of the 3-brane tension $V$ and the matter density $\rho$. The behavior of the background solution is consistent with the results based on the form of the 4D effective potential. Although the range of variation in $\rho_{b}$ is strongly constrained, the big bang nucleosynthesis bound on the time variation of the renormalized Newton constant $G_N = (8\pi M_P^2)^{-1}$ is satisfied when the ratio $V/\rho \gtrsim {O} (10^2)$ on cosmological scales. The same bound leads to an effective equation of state close to -1 at late epochs in accordance with current astrophysical and cosmological observations.Comment: 5 pages, 3 figures; v2: version to be published in PR

We Probably Live On An Inflating Brane-World

Brane-world models where observers are trapped within the thickness of a 3-brane offer novel perspectives on gravitation and cosmology. In this essay, I would argue that the problem of a late epoch acceleration of the universe is well explained in the framework of a 4-dimensional de Sitter universe embedded in a 5-dimensional de Sitter spacetime. While a 5D anti de Sitter space background is important for studying conformal field theories -- for its role in the AdS/CFT correspondence -- the existence of a 5-dimensional de Sitter space is crucial for finding an effective 4D Newton constant that remains finite and a normalizable zero-mode graviton wave function.Comment: 8 pages, latex (Essay received Honourable mention in Gravity Research Foundation essay competition 2011