Large scale anisotropy in Cosmic microwave Large scale anisotropy in Cosmic microwave background radiation background radiation Pranati Rath Under the Supervision of Prof.Pankaj Jain Pranati Rath Under the Supervision of Prof.Pankaj Jain DEPARTMENT OF PHYSICS Indian Institute of Technology, Kanpur January 21, 2015 1 / 56
Large scale Outline anisotropy in Cosmic microwave background radiation Pranati Rath Under the Supervision of Introduction Prof.Pankaj Jain Brief Review of CMB. CMB anomalies seen in data. Theoretical Models to explain anisotropy Anisotropic metric, direction dependent power spectrum Dipole Modulation in CMB or The hemispherical Power asymmetry. Theoretical Models for hemispherical Power asymmetry . Inhomogeneous Power spectrum model . Anisotropy Power spectrum model . Conclusion . 2 / 56
Large scale Introduction anisotropy in Cosmic microwave Cosmological Principle background radiation Pranati Rath Under the Supervision of Prof.Pankaj Jain Modern Cosmology based on Cosmological Principle which states that Universe is homogeneous and isotropic on large scales ( ≥ 100Mpc). Supported by High degree of isotropy seen in the CMB blackbody spectrum at a mean temperature of 2.725 K with a peak in the microwave regime. 3 / 56
Large scale Continued... anisotropy in Cosmic microwave Brief review of CMB background radiation Pranati Rath Under the Supervision of The observed CMB support the Prof.Pankaj Jain Hot Big Bang cosmological model. Photons were in thermal equilibrium with the inhomogeneous baryon density field upto the redshift z = 1100 Expansion of universe leads to formation of bound states (”Recombination”). After this epoch the photon mean free path increased to greater than the present Hubble radius so that they could free stream to us. Last scattering surface 4 / 56
Large scale Continued... anisotropy in Cosmic microwave background radiation Pranati Rath Under the Supervision of Prof.Pankaj Jain The COBE spacecraft detected the anisotropy in CMB which carries an imprint of the primordial perturbations via small temperature fluctuation of the order of 10 ( − 5) on angular scales > 7 o . 5 / 56
Large scale Continued... anisotropy in Cosmic microwave background radiation Pranati Rath Universe at Large Distance Scale Under the Supervision of Prof.Pankaj Jain CMB seen by Planck (380,000 years old universe), fluctuate 1 part in 100,000. 6 / 56
Large scale Continued... anisotropy in Cosmic microwave CMB Anomalies background radiation Pranati Rath Under the Supervision of Prof.Pankaj Jain Alignment of l = 2 , 3 multipoles of the cosmic microwave background radiation with significance 3 − 4 σ . Costa et al. 2004, Ralston & Jain 2004 Hemispherical power asymmetry or Dipole modulation in temperature. Eriksen et al. 2004, Hoftuft et al. 2009. Bennett et al. 2011, Ade et al. 2014 Parity asymmetry in the CMB data. Kim et al. 2010, Aluri & Jain 2012a Cold spot in CMB of radius 10 o located at l = 207 o and b = − 56 o in the Southern hemisphere. Vielva et al. 2004, Cruz et al. 2005 7 / 56
Large scale Continued... anisotropy in Cosmic microwave background radiation Pranati Rath Under the Supervision of Prof.Pankaj Jain Dipole anisotropy in radio polarizations. Birch 1982, Jain & Ralston 1999 Large scale alignment of optical polarizations. Hutsemekers 1998 Dipole anisotropy in distribution of radio galaxies Singal 2011, Tiwari et al. 2015 and cluster peculiar velocities Kashlinsky et al. 2010 . 8 / 56
Large scale Continued... anisotropy in Cosmic microwave background radiation Pranati Rath Under the Supervision of Prof.Pankaj Jain Remarkably several of these indicate a preferred direction towards the Virgo cluster . The indications for a preferred direction in the data have motivated many theoretical studies of inflationary models which violate statistical isotropy and homogeneity, giving rise to a direction dependent power spectrum . 9 / 56
Large scale continued... anisotropy in Cosmic microwave Theoretical models... background radiation Pranati Rath Under the Supervision of Prof.Pankaj Jain At very early times the Universe may be anisotropic and inhomogeneous. Bianchi models are for homogeneous, but anisotropic universes. � 3 For times t < t iso (= Λ ), the universe is anisotropic and becomes isotropic later on. Modes generated during this anisotropic phase leave the horizon at early times. Aluri & Jain 2012b . They re-enter the horizon later during radiation and dark matter dominated phases and leads to structure formation and CMB anisotropies. 10 / 56
Large scale Continued... anisotropy in Cosmic microwave Our Work... background radiation Pranati Rath Under the Supervision of Prof.Pankaj Jain We revisit, the two of the anomalies observed in the CMBR temperature data which is provided by WMAP and recently by PLANCK team. Alignment of the quadrupole ( l = 2) and octopole( l = 3). Hemispherical power asymmetry. 11 / 56
Large scale Continued... anisotropy in Cosmic microwave Alignment of quadrupole and octopole... background radiation Pranati Rath Under the Supervision of Prof.Pankaj Jain We show that the anisotropic modes arising during the very early phase of inflation can consistently explain the alignment of CMB quadrupole and octopole within the framework of Big Bang cosmology. 12 / 56
Large scale Continued... anisotropy in Cosmic microwave Anisotropic metric... background radiation Pranati Rath Under the Supervision of Prof.Pankaj Jain We consider three different anisotropic metrices, ds 2 = dt 2 − 2 √ σ dzdt − a 2 ( t )( dx 2 + dy 2 + dz 2 ) Model I ds 2 = dt 2 − a 2 ( t )( dx 2 + dy 2 ) − b 2 ( t ) dz 2 ) Model I ds 2 = dt 2 − a 2 1 ( t )( dx 2 + dy 2 ) − a 2 2 ( t ) dz 2 Model III where a 2 ( t ) = a 1 ( t ) + σ , σ being a constant, independent of time. 13 / 56
Large scale Continued... anisotropy in Cosmic microwave Quantization of field background radiation The action may be written as, Pranati Rath Under the Supervision of � Prof.Pankaj Jain d 4 x L S φ = and the Lagrangian density, L = 1 √− gg µν ∂ µ φ∂ ν φ . 2 The Quantized scalar field φ ( x , t ) in fourier space, d 3 k � � e i � x φ k ( t ) a k + e − i � � k · � k · � k ( t ) a † x φ ∗ φ I ( x , t ) = . (2 π ) 3 k k ′ ] = (2 π ) 3 δ ( k − k ′ ). with [ a k , a + Euler-Lagrange equation of motion, √− g ∂ ν ( g µν √− g ∂ µ φ ) = 0 . 1 14 / 56
Large scale Continued... anisotropy in Cosmic microwave Direction dependent power spectrum background radiation Pranati Rath Under the Model I Supervision of Prof.Pankaj Jain The Hamiltonian in interaction-picture, d 3 x √ σ � d φ I ( x , η ) � � d φ I ( x , η ) H I = . d η dz Two point correlations to first order, � φ ( x 1 , t ) φ ( x 2 , t ) � ≡ � φ I ( x 1 , t ) φ I ( x 2 , t ) � + � t dt ′ � [ H I ( t ′ ) , φ I ( x 1 , t ) φ I ( x 2 , t )] � . i 0 To the leading order of the perturbation the anisotropic part of the two point correlation vanishes, hence gives no correction to the primordial power spectrum. 15 / 56
Large scale Continued... anisotropy in Cosmic microwave background radiation Model II Pranati Rath Under the The power spectrum obtained in Ackerman et al. 2007 , Supervision of Prof.Pankaj Jain � n ) 2 � 1 + g ( k )(ˆ P ′ ( k ) = P iso ( k ) k · ˆ Model II The anisotropic function, g ( k ), at the end of inflation (time t ∗ ) is, g ( k ) = 9 � q ( t ∗ ) � 2 ǫ H log , ¯ H � � with, ¯ H = 1 3 (2 H a + H b ), ǫ H = 2 H b − H a and the physical ¯ 3 H k wavelength q ( t ∗ ) = a ( t ∗ ) . Here the perturbative correction to the isotropic power spectrum is neglected. 16 / 56
Model III Large scale anisotropy in Cosmic Similarly for model III, the modified power spectrum is given by, microwave background radiation � � Pranati Rath 1 + (ˆ P ′ ( k ) = P ′ k · z ) 2 g ( k ) iso ( k ) , Under the Supervision of Prof.Pankaj Jain where, � 2 k � 2 k � 2 k � � � �� g ( k ) = − σ − 5 2 a I ¯ + 2 a I ¯ k cos H sin H Si a I ¯ a I ¯ a I ¯ a I k H H H with � x d x ′ sin x ′ Si ( x ) ≡ . x ′ 0 Here P ′ iso ( k ), includes a perturbative correction to P iso ( k ) as � � 1 − g ( k ) P ′ iso ( k ) = P iso ( k ) . 3 17 / 56
Large scale Continued.. anisotropy in Cosmic microwave Effect of the power spectrum on the CMB background radiation Pranati Rath Temperature fluctuation, Under the Supervision of Prof.Pankaj Jain � 2 l + 1 � ( − i ) l P l (ˆ δ T (ˆ n ) = T 0 k · ˆ n ) δ ( k )Θ l ( k ) dk 4 π l For the low- l multipoles, only the Sachs-Wolfe effect contributes 3 effectively to the transfer function, Θ l ( k ) = 10 j l ( k η 0 ). Spherical harmonic coefficients a lm , � d Ω Y ∗ a lm = lm (ˆ n ) δ T (ˆ n ) . Two point correlation function of a lm ’s implies, � a lm a ∗ l ′ m ′ � = � a lm a ∗ l ′ m ′ � iso + � a lm a ∗ l ′ m ′ � aniso . 18 / 56
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