ANISOTROPIC UNIVERSE WITH ANISOTROPIC SOURCES PASCOS-2014, WARSAW ANISOTROPIC UNIVERSE WITH ANISOTROPIC SOURCES PASCOS-2014, WARSAW - - MANABENDRA SHARMA, IISER BHOPAL Work done with P. Aluri, S. Panda, S. Thakur JCAP 12, 003 (2013)

Standard Model of Cosmology: Universe governed by GTR on large scale, Isotropic and homogeneous spacetime. We consider a homogeneous but anisotropic spacetime Isotropic Universe Isotropic Sources with Ani sotropic Sources Anisotropic Universe with WHY DO WE CONSIDER IT ? HOW DOES IT LOOK LIKE ? HOW GOOD?

 Motivation….(why?)  How Does it look like? 1. EFE ( Bianchi-I universe & Anisotropic matter) 2. Null geodesic evolution 3. Fixed point analysis  A more realistic scenario  Temperature patterns  SN Ia constraints ……(How Good?)  Conclusion

Lambda CDM model, though successful, have drawbacks. In particular, Suppression of power at large angular scales (reduction of quadruple), alignment of quadruple and octuple roughly in the direction of virgo cluster, even odd power asymmetry are few example..(Not consistent with Lambda CDM Model) Observed low quadruple power can be explained in Bianchi-I model (Constraint on shear ) Campanelli, 2007 Is there any preferred direction derived from supernovae data? Also put constraints on anisotropic matter density and shear These reasons motivate us to adopt a metric in which one direction (longitudinal) expands differently from the other two. This can be achieved by a simple modification of the usual FRW model: (Bianchi I with planar symmetry) To produce reasonable amount of shear we consider anisotropic sources (AS) such as Magnetic Field, Cosmic Strings, Domain Walls and Lorentz violating magnetic field. Lambda CDM model, though successful, have drawbacks. In particular, Suppression of power at large angular scales (reduction of quadruple), alignment of quadruple and octuple roughly in the direction of virgo cluster, even odd power asymmetry are few example..(Not consistent with Lambda CDM Model) Observed low quadruple power can be explained in Bianchi-I model (Constraint on shear ) Campanelli, 2007 Is there any preferred direction derived from supernovae data? Also put constraints on anisotropic matter density and shear These reasons motivate us to adopt a metric in which one direction (longitudinal) expands differently from the other two. This can be achieved by a simple modification of the usual FRW model: (Bianchi I with planar symmetry) To produce reasonable amount of shear we consider anisotropic sources (AS) such as Magnetic Field, Cosmic Strings, Domain Walls and Lorentz violating magnetic field.

Cosmic String, Domain Walls (CS,DW): These are topological defects formed in the process of phase transition where Spontaneous Symmetry was broken in the early universe. CS is one dimensional whereas DW is two dimensional. Ref [1]. We consider homogeneous distribution of static CS parallel to the x axis throughout the y-z plane and planar DW in the y z plane perpendicular to the x axis. Magnetic Field: We consider a uniform magnetic field directed along x axis (Ref [2]) Lorentz Violating Magnetic Field: A microgauss magnetic field could be present which would have been produced due to lorentz- violating term in the photon sector. (Ref[3]) [1] E.W. Kolb and M.S. Turner, The Early Universe [2] L. Campanelli, Phys. Rev. D 76, [3] L. Campanelli, Phys. Rev. D 80, Cosmic String, Domain Walls (CS,DW): These are topological defects formed in the process of phase transition where Spontaneous Symmetry was broken in the early universe. CS is one dimensional whereas DW is two dimensional. Ref [1]. We consider homogeneous distribution of static CS parallel to the x axis throughout the y-z plane and planar DW in the y z plane perpendicular to the x axis. Magnetic Field: We consider a uniform magnetic field directed along x axis (Ref [2]) Lorentz Violating Magnetic Field: A microgauss magnetic field could be present which would have been produced due to lorentz- violating term in the photon sector. (Ref[3]) [1] E.W. Kolb and M.S. Turner, The Early Universe [2] L. Campanelli, Phys. Rev. D 76, [3] L. Campanelli, Phys. Rev. D 80,

Equation of state for Anisotropic Sources: Equation of state is defined as Matter Magnetic Field 1 2 1/3 Cosmic String /3 Domain Walls 0 -2/3 LVMF 1 0 1/3

Bianchi I metric with planar symmetry: EFE in this background with AS are: T he cont. eqn. for AS: Writing in terms of averaged Hubble parameter and shear With a redefinition of variable

Evolution of H' Evolution of h' Evolution of ρ' Evolution of H' Evolution of h' Matter1+3w MF2 CS0 DW LVMF2

Constraint

Defining τ as equation for Hubble parameter is Deceleration parameter: Eqn. For shear: Constraint: where,, Geodesic Equation: with

Thus in the asymptotic limit state variables approach towards their stable fixed points.

Modified Friedmann Equation: (All Omegas are mutually decoupled, follow their own cont. eqn.) IsotropicMatter, Dust Anisotropic Sources Cosmological Constant Shear

Evolution of Dynamical variables 1.Eventually dominated by CC 2.q negative at late time 3.Universe isotropize at late times 4.Appreciable shear in DW in the intermediate time

Temperature Patterns It has been shown earlier that the total quadrupole anisotropy in the presence of a uniform magnetic field, can be small compared to that obtained from the standard LCDM model Campanelli, 2007 The temperature of the cosmic microwave background as a function of the angular coordinates on the celestial sphere is given by Lim, 1999 :Mean isotropic temperature at last scattering surface The direction cosines along a null geodesic in terms of the spherical polar angles are given by

(…how good?) SN Ia Constraints Line element: Anisotropic axis along z-dirn Mean scale factor: Eccentricity: The redshift (z) and luminosity distance ( ) of an SN1a object observed in the direction Theoretical distance modulus: Where k is dimensionfull and h being the dimensionless Hubble parameter is the angle between the cosmic preferred axis and the supernova position Constrain the level of fractional energy density, shear and also determine the cosmic preferred axis if any.

minimization in order to put constraints on the parameters: :measured distance modulus of an SN1a object from data :theoretical distance modulus function involving various cosmological parameters :measured uncertainty in the distance modulus of an SN1a object provided in the data (Summation is over all SN1a objects (total 557 supernovae) The luminosity distance,, (and thus the distance modulus ) depends on all the cosmological parameters The minimization is done in conjugation with solving the evolution equations:

Equations are evolved from for each supernova i with the initial conditions at as, corresponding to the choice and and random guess values for the parameters to do the minimization. The deceleration parameter is given by. Compared with standard concordance model using luminosity distance relation

CS DW MF LVMF And confidence regions are shown in black solid lines Likelihoods of anisotropy axis

 We examine evolution of EFE  We determine the stable fixed points of the full set of evolution equations including the geodesic equations in tau time and also checked their stability. Isotropization at late time takes place for all cases of anisotropic sources.  To make it a more realistic scenario, we include ordinary isotropic dark matter and cosmological constant as dark energy. We found that the universe asymptotically evolves to a de Sitter universe. Isotropization takes place at late times in this case too.  We generate temperature patterns for realistic scenarios.  We also constrain the parameters of this model using Supernovae Union 2 data and found a preferred axis from the data for all the four cases of anisotropic matter. This axis is very close to the mirror symmetry axis found in CMB data.

We thank Santanu das for sharing his MCMC cosmological parameter estimation code. We also acknowledge the use of Healpix and Eran Ofek's MATLAB routine coco.m for astronomical co-ordinate conversion of SN1a positions, in this work.

 Precise Measurement of the temp. anisotropies of the CMB is very well explained by LCDM model.  Any departure from LCDM model are small and of uncertain statistical significance. However several anomalies are observed.  CMB Anomalies: Suppression of power at large angular scales, alignment of quadrupole and octopole roughly in the direction of virgo cluster, ecliptic north south power asymmetry, presence of cold spot, mirror symmetry/asymmetry, dark energy dipole, fine structure dipole, peculiar velocity dipole, maximum temp. asymmetry etc.  Observed Quadrupole Power LCDM gives a value  Can be explained in Bianchi-I model Constraint on shear Campanelli, 2006  In a global anisotropic universe, isotropisation occurs very fast during inflation To induce any appreciable amount of shear, at LSS, anisotropic source Is required.  Observed quadrupole power in Bianchi l universe Large polarisation P. Cea, 2014  Using very distant supernovae as standard candles, one can trace the history of cosmic expansion and try to find out what’s currently speeding it up.  shear. Is there any preferred direction derived from supernovae data? Also put constraints on anisotropic matter density and

CMB: relic photons decoupled from the rest of the matter in the early universe. Formed when the universe was just 2,00,000 years old, since then moving freely and still present today (the current age 14 billion years) Last Scattering Surface. A perfectly black body spectrum, wavelength red shifted away as the universe expands, Mean temperature today: 2.73 K In an FRW background we expect an uniform, isotropic CMB distribution As any function on the sphere can be expressed in the basis set of spherical harmonics, so thus the temperature distribution function. While doing multipole expansion of the temperature distribution, it has been realized that an exactly FRW background is not compatible with the observation.

CMB: relic photons decoupled from the rest of the matter in the early universe. Formed when the universe was just 2,00,000 years old, since then moving freely and still present today (the current age 14 billion years) Last Scattering Surface. A perfectly black body spectrum, wavelength red shifted away as the universe expands, Mean temperature today: 2.73 K In an FRW background we expect an uniform, isotropic CMB distribution As any function on the sphere can be expressed in the basis set of spherical harmonics, so thus the temperature distribution function. While doing multipole expansion of the temperature distribution, it has been realized that an exactly FRW background is not compatible with the observation.

Bianchi I metric with planner symmetry: EFE in this background with AS are: T he continuity equation is for AS: Modified Friedmann Equation Where averaged Hubble parameter and shear With a redefinition of variable

σ Vs τ Ω Vs τ

K3 Vs τ K1 Vs τ

What does it do ? Null Geodesic Equation: with Equations have been evolved numerically by imposing the constraint equation at each point. This approach helps us to write the geodesic equation as a first order differential equation in contrast to the metric approach where they are second order. Where is the energy of photon, and are the three components of photon momentum. The constraint equation Consider a case: decreases slowly for magnetic field and faster for walls. and also evolve in a similar manner, except for the interchange of evolution of cosmic strings and LVMF.

Thus in the asymptotic limit state variables approach towards their stable fixed points. Matter σ (K1, K2, K3) Magnetic Field 1 ( ± 1,0,0) Cosmic String 1/2 ( ± 1,0,0) Domain Walls -2/5 0, ±1/(√2), ±1/(√2) LVMF 0, ±1/(√2), ±1/(√2)

Deceleration parameter q changes from 1/2 to -1 as we move from ordinary DM dominated era to recent DE dominated era Isotropisation takes place at late times. Late time behaviour in all these cases is almost same except for domain walls. However small may be the value of to start with, it turns out that tends to rise at intermediate times, and can even dominates over isotropic matter at present time for some initial values. Evolution

The luminosity distance,, (and thus the distance modulus ) depends on all the cosmological parameters The minimization is done in conjugation with solving the evolution equations The ’denotes a derivative with respect to

The reference coordinate system is galactic coordinate system

Anisotropic Sources A network of domain walls can be formed during the phase transition in the early universe by spontaneous breaking of a symmetry, separated by a distance of the order of correlation length. In a self interacting real scalar field theory for a domain wall (in yz-plane), the energy momentum (e-m) tensor takes the form where A(x) has a bell shaped distribution around x=0. The wall can be made thin by appropriately tuning the coupling strength and the vacuum expectation value of the self interacting scalar field. A network of N planar domain walls with a box of volume V. Let us assume that the walls of this stack reside at points on the x-axis. Then the total e-m tensor for such a network of non-interacting walls is given by Domain walls

In the case of a large N, we can have a function g(x) which is the average number of walls per unit length in the range x and x+dx. It is normalized to satisfy Then the average e-m tensor of this configuration With an average distance between the walls as d, we can approximate the average e-m tensor as : surface energy density For slowly moving domain walls

Cosmic Strings it is well known that a network of cosmic strings can be formed during the phase transition in the early universe when a U(1) symmetry is broken. The e-m tensor due to an infinite string with mass per unit length along the x-direction: The average e-m tensor for a network of slowly moving cosmic strings along a particular direction approximated by d: the average separation between the cosmic strings Actual evolution of these networks is complicated.