Branes and Inflationary Cosmology

Abstract

We discuss a brane based inflationary scenario in which an initially non-supersymmetric configuration involving a D4 brane is dynamically transformed into a supersymmteric one in a background space-time geometry determined by a stack of D6 branes. Inflation is realized in the effective four dimensional theory and ends after reaching a stable BPS configuration. The scalar spectral index turns out to be 0.98. Under some simplifying assumption the reheat temperature, Hubble constant and the string scale are estimated to be of order $10^{8}$ GeV, $10^{12}$ GeV and $10^{16}$ GeV, respectively.

Figures (4)

• Figure 1: Various supersymmetric configurations of branes. ${\bf (a)}$ A Dp brane in directions ($x_0, \cdots, x_p$) ends in the direction $x_p$ on a D(p+2) brane in directions ($x_0, \cdots, x_{p-1},x_{p+1}, x_{p+2}, x_{p+3}$). ${\bf (b)}$ A Dp brane in directions ($x_0, \cdots, x_{p-1}, x_6$) ends in the direction $x_6$ on a NS5 brane in directions ($x_0, \cdots, x_5$). ${\bf (c)}$ A Dp brane with world volume in directions ($x_0, \cdots, x_p$) and a D(p+2) brane in directions ($x_0, \cdots, x_{p-1}, x_{p+1}, x_{p+2}, x_{p+3}$). ${\bf (d)}$ A Dp brane is partially orthogonal to a NS5 brane. ${\bf (e)}$ A Dp brane in directions ($x_0, \cdots, x_p$) is parallel to a D(p+4) brane along ($x_0, \cdots, x_{p+4}$). ${\bf (f)}$ Two Dp branes are stretched in the same directions. In ${\bf (c)}$-- ${\bf (f)}$, dotted lines indicate separation between branes. While the configurations ${\bf (a)}$--${\bf (g)}$ preserve 8 supercharges, ${\bf (f)}$ preseves 16 supercharges. A Dp brane intersecting a D(p+2) brane as in ${\bf (g)}$ can split into two disconnected parts as in ${\bf (h)}$, which separate along the D(p+2) brane.
• Figure 2: Supersymmetric Configuration. This configuration preserves 8 supercharges.
• Figure 3: Initial Configuration. ${\bf (a)}$ Non-zero $\theta$ breaks supersymmetry. $r$ is the distance between D6 and D4 branes. ${\bf (b)}$ shows the same configuration as ${\bf (a)}$. $x_{6'}$ and $x_{7'}$ are the coordinates $x_6$ and $x_7$ rotated by $\theta$ around $x_4$ and/or $x_5$. An O$4^-$ plane is located on $x_7=l$. In toroidal compactification, a--f and g--j are identified.
• Figure 4: Final Configuration. ${\bf (a)}$ D4 brane is split and takes minimum length configuration between D6 and NS5 branes. At the minimum of the potential, supersymmetry is restored. ${\bf (b)}$ shows the same configuration as in ${\bf (a)}$.