[Paper Review] D-branes and cosmic structure

D. WILLS, Konstantinos Dimopoulos+1 more|arXiv (Cornell University)|Mar 22, 2013

Cosmology and Gravitation Theories14 references3 citations

TL;DR

This paper proposes embedding the vector curvaton scenario in Type IIB string theory, where a D-brane vector field generates primordial curvature perturbations via gravitational particle production. By tuning the gauge kinetic function and mass to scale as $ f \propto a(t)^{-4} $ and $ m \propto a(t) $, the model yields a scale-invariant spectrum of superhorizon perturbations, enabling viable cosmic structure formation in both open and closed string inflation contexts.

ABSTRACT

We outline the embedding of the vector curvaton scenario as a promising mechanism to generate statistical anisotropy within Type IIB string theory, where the vector field on a single D-brane plays the role of the vector curvaton. We first consider a toy model in the context of open string inflation, and then begin to construct a concrete model in the context of closed string inflation.

Motivation & Objective

• To explore whether D-brane vector fields in Type IIB string theory can serve as curvatons, generating primordial density fluctuations without driving inflation.
• To investigate the feasibility of realizing statistical anisotropy in the cosmic microwave background through vector curvaton mechanisms in string-theoretic settings.
• To construct a concrete model in closed string inflation using D7-branes, where the vector field on the brane acts as the curvaton.
• To ensure the resulting perturbation spectrum is scale-invariant and consistent with CMB observations.
• To verify that the required scaling of mass and gauge kinetic function can be realized in a consistent string compactification with stabilized moduli.

Proposed method

• Formulate the effective Lagrangian for a massive Abelian vector field with a time-dependent gauge kinetic function $ f $ and mass $ m $, using the DBI and Wess-Zumino actions on D-branes.
• Derive the equations of motion for the homogeneous vector field and its quantum perturbations in an FRW background, identifying the canonically normalized physical field $ W = \sqrt{f}A/a $.
• Compute the superhorizon power spectra for transverse and longitudinal polarizations of the vector field perturbations using the mode equations in momentum space.
• Impose the scaling conditions $ m \propto a(t) $ and $ f \propto a(t)^{-4} $ to achieve a scale-invariant power spectrum, as required by CMB observations.
• Analyze the dynamics of the inflaton and vector field in closed string inflation, assuming negligible backreaction and a slowly varying inflaton field $ \chi \propto a(t)^{-3} $.
• Verify that the required scaling of $ f \propto a(t)^{-4} $ is realizable via the D7-brane worldvolume action, with $ f = \tau $ and $ m \propto \tau^{-1/4} $, where $ \tau $ is the D7-brane volume modulus.

Experimental results

Research questions

• RQ1 Can a D-brane vector field in Type IIB string theory generate a scale-invariant curvature perturbation spectrum via gravitational particle production?
• RQ2 What specific scaling behavior of the gauge kinetic function $ f $ and vector field mass $ m $ is required for the vector curvaton to produce an observationally viable spectrum?
• RQ3 Is it possible to realize the required $ f \propto a(t)^{-4} $ and $ m \propto a(t) $ scaling in a concrete closed string inflation model with D7-branes?
• RQ4 How does the backreaction of the vector field onto the inflaton field affect the viability of the curvaton scenario in string compactifications?
• RQ5 Can the required field range for the inflaton $ \chi \propto a(t)^{-3} $ be realized in a realistic compactification with stabilized moduli?

Key findings

• The vector curvaton scenario can be realized in Type IIB string theory using a D-brane vector field, with the vector field on a D3-brane serving as a toy model in open string inflation.
• For the D7-brane in closed string inflation, the gauge kinetic function $ f = \tau $ and mass $ m \propto \tau^{-1/4} $ lead to $ f \propto a(t)^{-4} $ and $ m \propto a(t) $, satisfying the condition for a scale-invariant spectrum.
• The superhorizon power spectra for transverse and longitudinal modes are found to be scale-invariant when $ f \propto a(t)^{-4} $ and $ m \propto a(t) $, as required by CMB observations.
• The model requires the inflaton field $ \chi $ to scale as $ \chi \propto a(t)^{-3} $, which is consistent with a slowly varying potential and negligible backreaction.
• The initial conditions must satisfy $ \dot{\chi}_0 \lesssim -3H_0\chi_0 $ and $ \chi_0 \ll \sqrt{2/3} $ to ensure sub-Planckian initial values and a long enough field range for inflation.
• The model is viable only if the stabilised value of $ \chi $ is small and the field evolution is dominated by the exponential decay $ \chi \propto e^{-3Ht} $, which requires careful tuning of initial conditions and moduli stabilization.