(RESCEU &IPMU ) 横山順一

Inflaton φ slow rollover Reheating V[φ] BEGINNING?? END?? Λ But little is known about the beginning and end of inflation. Slow-roll phase is now probed by astronomical observations. Klein Gordon Equation Einstein Equation Cosmic Scale Factor Hubble parameter

Fluctuation is generated continuously in each Hubble time with initial wavelength and amplitude which is stretched by exponential expansion. depends on the potential and its derivative. Since the right-hand-side evolves very slowly, we find a nearly scale-invariant spectrum. time scale H -1 during inflation The modes which left the Hubble horizon earlier are stretched more to constitute longer wavelength modes.

： polarization tensor with satisfies the same eqn as a minimally coupled massless scalar field. Long-wave quantum fluctuation is generated during inflation. A for

Square amplitude of tensor perturbation 2 polarization modes of the graviton = 2 independent massless fields Square amplitude per logarithmic frequency interval Tensor perturbation has a nearly scale-invariant spectrum at formation.

curvature perturbation tensor/scalar ratio spectral index and its running (scale dependence)

-200 T(μK) +200

Low frequency components of tensor perturbations may be observed by B-mode polarization of CMB anisotropy Polarization is generated by quadrupole temperature anisotropy. E-mode from both scalar (density) and tensor perturbations. B-mode only from tensor perturbations. E mode B mode Ongoing/Planned projects and their target sensitivity PLANCK ｒ ～ 0.1 BICEP ｒ ～ 0.05 PolarBear ｒ ～ 0.01 QUIET ｒ ～ 0.01 CLOVER ｒ ～ 0.01 EPIC ｒ ～ B-POL ｒ ～ 0.001

High frequency components may be observed by future space-based laser interferometers. Deci-hertz Interferometer Gravitational Wave Observatory N. Seto, S. Kawamura, & T. Nakamura, PRL 87(2001) amplitude of GW to achieve S/N>1 after ten years of correlation analysis DECIGO ©cooray.org

In terms of B-mode polarization, we can measure around the wavenumber corresponding to. inflaton field value when comoving scale corresponding to large-scale CMB observation ( ) left the Hubble radius during inflation inflaton field value when comoving scale corresponding to frequency f today left the Hubble radius during inflation # of e-folds between the two epochs. We can extrapolate to using slow-roll parameters at. This gives the initial amplitude of gravitational radiation when the mode with comoving frequency f reentered the Hubble radius at.

なので、 CMB スケールに対応する から 以下のように展開できる。 などにより、 と求まる。

Amplitude of GW is constant when its wavelength is longer than the Hubble radius between and. scale time H -1 a(t) λ inflation Hubble horizon After entering the Hubble radius, the wavelength decreases as and the energy density as. H -1 Radiation dominant Matter dominant When, the tensor perturbation evolves as

Density parameter in GW per logarithmic frequency interval When the mode reentered the Hubble horizon at, the angular frequency is equal to, so we find

ハッブルホライズンに入ったあとには、 : equation of state 放射優勢期には、これは一定である。 放射優勢期にホライズンに入ったモードは初期のスペクトルの形状 をそのまま留めている。 標準宇宙論では、今日周波数 f のモードがホライズンに入った ときの宇宙の温度は、 インフレーション後の再加熱温度がこれより高ければ、生成時の スペクトルがそのまま DECIGO によって観測されるであろう。

UC U C

After entering the Hubble horizon, : equation of state During radiation domination, it is constant. We can probe the change of the equation of state. Evolution of the density parameter (Seto & JY 03)

can be determined by large-scale observations can be observed by DECIGO/BBO We can determine the equation of state in the early Universe. We can determine thermal history of the early Universe. reheating temperature after inflation

再加熱温度が低い場合はスペクトルが変形する。

水色：重力波を検出できる領域 空色：さらに再加熱温度も決定 できる領域

CMB の B モード偏光が検出できると、 DECIGO 帯の重力波を予言できる DECIGO によって再加熱時期が観測できる Ongoing/Planned projects and their target sensitivity PLANCK ｒ ～ 0.1 BICEP ｒ ～ 0.05 PolarBear ｒ ～ 0.01 QUIET ｒ ～ 0.01 CLOVER ｒ ～ 0.01 EPIC ｒ ～ B-POL ｒ ～ 0.001