Searching for Cosmic Strings in New Obervational Windows
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1 1 / 42 Searching for s in New Obervational Windows Robert Brandenberger McGill University Sept. 28, 2010
2 2 / 42 Outline s in 5
3 3 / 42 Plan s in 5
4 s T. Kibble, J. Phys. A 9, 1387 (1976); Y. B. Zeldovich, Mon. Not. Roy. Astron. Soc. 192, 663 (1980); A. Vilenkin, Phys. Rev. Lett. 46, 1169 (1981). 4 / 42 string = linear topological defect in a quantum field theory. 1st analog: line defect in a crystal 2nd analog: vortex line in superfluid or superconductor string = line of trapped energy density in a quantum field theory. Trapped energy density gravitational effects on space-time important in cosmology.
5 s T. Kibble, J. Phys. A 9, 1387 (1976); Y. B. Zeldovich, Mon. Not. Roy. Astron. Soc. 192, 663 (1980); A. Vilenkin, Phys. Rev. Lett. 46, 1169 (1981). 4 / 42 string = linear topological defect in a quantum field theory. 1st analog: line defect in a crystal 2nd analog: vortex line in superfluid or superconductor string = line of trapped energy density in a quantum field theory. Trapped energy density gravitational effects on space-time important in cosmology.
6 s T. Kibble, J. Phys. A 9, 1387 (1976); Y. B. Zeldovich, Mon. Not. Roy. Astron. Soc. 192, 663 (1980); A. Vilenkin, Phys. Rev. Lett. 46, 1169 (1981). 4 / 42 string = linear topological defect in a quantum field theory. 1st analog: line defect in a crystal 2nd analog: vortex line in superfluid or superconductor string = line of trapped energy density in a quantum field theory. Trapped energy density gravitational effects on space-time important in cosmology.
7 It is interesting to find ways to possibly lower the bounds on the string tension. 5 / 42 Relevance to Cosmology I strings are predicted in many particle physics models beyond the Standard Model". strings are predicted to form at the end of inflation in many inflationary models. In models which admit cosmic strings, cosmic strings inevitably form in the early universe and persist to the present time. strings are constrained from cosmology: strings with a tension which is too large are in conflict with the observed acoustic oscillations in the CMB angular power spectrum. Existing upper bound on the string tension rules out large classes of particle physics models.
8 It is interesting to find ways to possibly lower the bounds on the string tension. 5 / 42 Relevance to Cosmology I strings are predicted in many particle physics models beyond the Standard Model". strings are predicted to form at the end of inflation in many inflationary models. In models which admit cosmic strings, cosmic strings inevitably form in the early universe and persist to the present time. strings are constrained from cosmology: strings with a tension which is too large are in conflict with the observed acoustic oscillations in the CMB angular power spectrum. Existing upper bound on the string tension rules out large classes of particle physics models.
9 It is interesting to find ways to possibly lower the bounds on the string tension. 5 / 42 Relevance to Cosmology I strings are predicted in many particle physics models beyond the Standard Model". strings are predicted to form at the end of inflation in many inflationary models. In models which admit cosmic strings, cosmic strings inevitably form in the early universe and persist to the present time. strings are constrained from cosmology: strings with a tension which is too large are in conflict with the observed acoustic oscillations in the CMB angular power spectrum. Existing upper bound on the string tension rules out large classes of particle physics models.
10 It is interesting to find ways to possibly lower the bounds on the string tension. 5 / 42 Relevance to Cosmology I strings are predicted in many particle physics models beyond the Standard Model". strings are predicted to form at the end of inflation in many inflationary models. In models which admit cosmic strings, cosmic strings inevitably form in the early universe and persist to the present time. strings are constrained from cosmology: strings with a tension which is too large are in conflict with the observed acoustic oscillations in the CMB angular power spectrum. Existing upper bound on the string tension rules out large classes of particle physics models.
11 6 / 42 Relevance to Cosmology II strings can produce many good things for cosmology: String-induced mechanism of baryogenesis (R.B., A-C. Davis and M. Hindmarsh, 1991). Explanation for the origin of primordial magnetic fields which are coherent on galactic scales (X.Zhang and R.B. (1999)). Explanation for cosmic ray anomalies (R.B., Y. Cai, W. Xue and X. Zhang (2009)). It is interesting to find evidence for the possible existence of cosmic strings.
12 6 / 42 Relevance to Cosmology II strings can produce many good things for cosmology: String-induced mechanism of baryogenesis (R.B., A-C. Davis and M. Hindmarsh, 1991). Explanation for the origin of primordial magnetic fields which are coherent on galactic scales (X.Zhang and R.B. (1999)). Explanation for cosmic ray anomalies (R.B., Y. Cai, W. Xue and X. Zhang (2009)). It is interesting to find evidence for the possible existence of cosmic strings.
13 7 / 42 Preview Important lessons from this talk: strings nonlinearities already at high redshifts. cosmic strings more pronounced at high redshifts. strings lead to perturbations which are non-gaussian. strings predict specific geometrical patterns in position space. 21 cm surveys provide an ideal arena to look for cosmic strings (R.B., R. Danos, O. Hernandez and G. Holder, 2010).
14 8 / 42 Plan s in 5
15 I A. Vilenkin and E. Shellard, s and other Topological Defects (Cambridge Univ. Press, Cambridge, 1994). 9 / 42 strings form after symmetry breaking phase transitions. Prototypical example: Complex scalar field φ with Mexican hat" potential: V (φ) = λ 4 ( φ 2 η 2) 2 Vacuum manifold M: set up field values which minimize V. (1)
16 I A. Vilenkin and E. Shellard, s and other Topological Defects (Cambridge Univ. Press, Cambridge, 1994). 9 / 42 strings form after symmetry breaking phase transitions. Prototypical example: Complex scalar field φ with Mexican hat" potential: V (φ) = λ 4 ( φ 2 η 2) 2 Vacuum manifold M: set up field values which minimize V. (1)
17 10 / 42 Scalar Field Potential
18 I A. Vilenkin and E. Shellard, s and other Topological Defects (Cambridge Univ. Press, Cambridge, 1994). 11 / 42 strings form after symmetry breaking phase transitions. Prototypical example: Complex scalar field φ with Mexican hat" potential: V (φ) = λ ( φ 2 η 2) 2 4 Vacuum manifold M: set up field values which minimize V. At high temperature: φ = 0. At low temperature: φ = η - but not at all x. string core: points with φ η. Criterium for the existence of cosmic strings: Π 1 (M). (2)
19 I A. Vilenkin and E. Shellard, s and other Topological Defects (Cambridge Univ. Press, Cambridge, 1994). 11 / 42 strings form after symmetry breaking phase transitions. Prototypical example: Complex scalar field φ with Mexican hat" potential: V (φ) = λ ( φ 2 η 2) 2 4 Vacuum manifold M: set up field values which minimize V. At high temperature: φ = 0. At low temperature: φ = η - but not at all x. string core: points with φ η. Criterium for the existence of cosmic strings: Π 1 (M). (2)
20 I A. Vilenkin and E. Shellard, s and other Topological Defects (Cambridge Univ. Press, Cambridge, 1994). 11 / 42 strings form after symmetry breaking phase transitions. Prototypical example: Complex scalar field φ with Mexican hat" potential: V (φ) = λ ( φ 2 η 2) 2 4 Vacuum manifold M: set up field values which minimize V. At high temperature: φ = 0. At low temperature: φ = η - but not at all x. string core: points with φ η. Criterium for the existence of cosmic strings: Π 1 (M). (2)
21 12 / 42 II Symmetric cosmic string configuration (uniform along z axis, with core at ρ = 0): Important features: Width w λ 1/2 η 1 φ(ρ, θ) = f (ρ)ηe iθ (3) f (ρ) 1 for ρ > w (4) f (ρ) 0 for ρ < w (5) Mass per unit length µ η 2 (independent of λ).
22 13 / 42 Formation of T. Kibble, Phys. Rept. 67, 183 (1980). By causality, the values of φ in M cannot be correlated on scales larger than t. Hence, there is a probability O(1) that there is a string passing through a surface of side length t. If the field φ is in thermal equilibrium above the phase transition temperature, then the actual correlation length of the string network (mean separation and curvature radius of the network of infinite strings) is microscopic, given by the Ginsburg length" λ 1 η 1.
23 13 / 42 Formation of T. Kibble, Phys. Rept. 67, 183 (1980). By causality, the values of φ in M cannot be correlated on scales larger than t. Hence, there is a probability O(1) that there is a string passing through a surface of side length t. If the field φ is in thermal equilibrium above the phase transition temperature, then the actual correlation length of the string network (mean separation and curvature radius of the network of infinite strings) is microscopic, given by the Ginsburg length" λ 1 η 1.
24 13 / 42 Formation of T. Kibble, Phys. Rept. 67, 183 (1980). By causality, the values of φ in M cannot be correlated on scales larger than t. Hence, there is a probability O(1) that there is a string passing through a surface of side length t. If the field φ is in thermal equilibrium above the phase transition temperature, then the actual correlation length of the string network (mean separation and curvature radius of the network of infinite strings) is microscopic, given by the Ginsburg length" λ 1 η 1.
25 14 / 42 Scaling Solution I Causality network of cosmic strings persists at all times. Correlation length ξ(t) < t for all times t > t c. Dynamics of ξ(t) is governed by a Boltzmann equation which describes the transfer of energy from long strings to string loops
26 14 / 42 Scaling Solution I Causality network of cosmic strings persists at all times. Correlation length ξ(t) < t for all times t > t c. Dynamics of ξ(t) is governed by a Boltzmann equation which describes the transfer of energy from long strings to string loops
27 Scaling Solution II R. H. Brandenberger, Int. J. Mod. Phys. A 9, 2117 (1994) [arxiv:astro-ph/ ]. Analysis of the Boltzmann equation shows that ξ(t) t for all t > t c : If ξ(t) << t then rapid loop production and ξ(t)/t increases. If ξ(t) >> t then no loop production and ξ(t)/t decreases. Sketch of the scaling solution: 15 / 42
28 16 / 42 History I strings were popular in the 1980 s as an alternative to inflation for producing a scale-invariant spectrum of cosmological perturbations. strings lead to incoherent and active fluctuations (rather than coherent and passive like in inflation). Reason: strings on super-hubble scales are entropy fluctuations which seed an adiabatic mode which is growing until Hubble radius crossing. Boomerang CMB data (1999) on the acoustic oscillations in the CMB angular power spectrum rules out cosmic strings as the main source of fluctuations.. Interest in cosmic strings collapses.
29 History II Supergravity models of inflation typically yield cosmic strings after reheating (R. Jeannerot et al., 2003). Brane inflation models typically yield cosmic strings in the form of cosmic superstrings (Sarangi and Tye, 2002). superstrings can also arise in the String Gas Cosmology alternative to inflation (A. Nayeri, R.B. and C. Vafa, 2006; R.B. 2008). renewed interest in cosmic strings as supplementary source of fluctuations. Best current limit from angular spectrum of CMB anisotropies: 10% of the total power can come from strings (see e.g. Wyman, Pogosian and Wasserman, 2005). Leads to limit Gµ < / 42
30 History II Supergravity models of inflation typically yield cosmic strings after reheating (R. Jeannerot et al., 2003). Brane inflation models typically yield cosmic strings in the form of cosmic superstrings (Sarangi and Tye, 2002). superstrings can also arise in the String Gas Cosmology alternative to inflation (A. Nayeri, R.B. and C. Vafa, 2006; R.B. 2008). renewed interest in cosmic strings as supplementary source of fluctuations. Best current limit from angular spectrum of CMB anisotropies: 10% of the total power can come from strings (see e.g. Wyman, Pogosian and Wasserman, 2005). Leads to limit Gµ < / 42
31 18 / 42 Plan s in 5
32 19 / 42 Geometry of a Straight String A. Vilenkin, Phys. Rev. D 23, 852 (1981). Space away from the string is locally flat (cosmic string exerts no gravitational pull). Space perpendicular to a string is conical with deficit angle α = 8πGµ, (6)
33 20 / 42 Effect N. Kaiser and A., Nature 310, 391 (1984). Photons passing by the string undergo a relative Doppler shift δt T = 8πγ(v)vGµ, (7)
34 21 / 42 network of line discontinuities in CMB anisotropy maps. N.B. characteristic scale: comoving Hubble radius at the time of recombination need good angular resolution to detect these edges. Need to analyze position space maps.
35 22 / 42 Signature in CMB temperature anisotropy maps R. J. Danos and R. H. Brandenberger, arxiv: [astro-ph] x 10 0 map of the sky at 1.5 resolution
36 23 / 42 network of line discontinuities in CMB anisotropy maps. Characteristic scale: comoving Hubble radius at the time of recombination need good angular resolution to detect these edges. Need to analyze position space maps. Edges produced by cosmic strings are masked by the background" noise.
37 24 / 42 Temperature map Gaussian + strings
38 network of line discontinuities in CMB anisotropy maps. Characteristic scale: comoving Hubble radius at the time of recombination need good angular resolution to detect these edges. Need to analyze position space maps. Edges produced by cosmic strings are masked by the background" noise. Edge detection algorithms: a promising way to search for strings Application of Canny edge detection algorithm to simulated data (SPT/ACT specification) limit Gµ < may be achievable [S. Amsel, J. Berger and R.B. (2007), A. Stewart and R.B. (2008), R. Danos and R.B. (2009)] 25 / 42
39 26 / 42 Wake J. Silk and A. Vilenkin, Phys. Rev. Lett. 53, 1700 (1984). Consider a cosmic string moving through the primordial gas: Wedge-shaped region of overdensity 2 builds up behind the moving string: wake.
40 Closer look at the wedge Consider a string at time t i [t rec < t i < t 0 ] moving with velocity v s with typical curvature radius c 1 t i 4!Gµtivs"s v c 1 t i t i v s "s 27 / 42
41 28 / 42 Gravitational accretion onto a wake L. Perivolaropoulos, R.B. and A., Phys. Rev. D 41, 1764 (1990). Initial overdensity gravitational accretion onto the wake. Accretion computed using the Zeldovich approximation. Focus on a mass shell a physical distance w(q, t) above the wake: w(q, t) = a(t) ( q ψ ), (8) Gravitational accretion ψ grows. Turnaround: ẇ(q, t) = 0 determines q nl (t) and thus the thickness of the gravitationally bound region.
42 28 / 42 Gravitational accretion onto a wake L. Perivolaropoulos, R.B. and A., Phys. Rev. D 41, 1764 (1990). Initial overdensity gravitational accretion onto the wake. Accretion computed using the Zeldovich approximation. Focus on a mass shell a physical distance w(q, t) above the wake: w(q, t) = a(t) ( q ψ ), (8) Gravitational accretion ψ grows. Turnaround: ẇ(q, t) = 0 determines q nl (t) and thus the thickness of the gravitationally bound region.
43 28 / 42 Gravitational accretion onto a wake L. Perivolaropoulos, R.B. and A., Phys. Rev. D 41, 1764 (1990). Initial overdensity gravitational accretion onto the wake. Accretion computed using the Zeldovich approximation. Focus on a mass shell a physical distance w(q, t) above the wake: w(q, t) = a(t) ( q ψ ), (8) Gravitational accretion ψ grows. Turnaround: ẇ(q, t) = 0 determines q nl (t) and thus the thickness of the gravitationally bound region.
44 29 / 42 Signature in CMB Polarization R. Danos, R.B. and G. Holder, arxiv: [astro-ph.co]. Wake is a region of enhanced free electrons. CMB photons emitted at the time of recombination acquire extra polarization when they pass through a wake. Statistically an equal strength of E-mode and B-mode polarization is generated. Consider photons which at time t pass through a string segment laid down at time t i < t. P Q 24π ( 3 ) 1/2σT fgµv s γ s 25 4π Ω B ρ c (t 0 )mp 1 ( ) 2 ( t 0 z(t) + 1 z(ti ) + 1 ) 1/2. (9)
45 30 / 42 Signature in CMB Polarization II Inserting numbers yields the result: P Q fgµv (z(t) + 1) 2 (z(t i ) + 1) 310 sγ s Ω 7 B (10) Characteristic pattern in position space:
46 31 / 42 Plan s in 5
47 32 / 42 Motivation 21 cm surveys: new window to map the high redshift universe, in particular the dark ages". strings produce nonlinear structures at high redshifts. These nonlinear structures will leave imprints in 21 cm maps. 21 cm surveys provide 3-d maps potentially more data than the CMB. 21 cm surveys is a promising window to search for cosmic strings.
48 32 / 42 Motivation 21 cm surveys: new window to map the high redshift universe, in particular the dark ages". strings produce nonlinear structures at high redshifts. These nonlinear structures will leave imprints in 21 cm maps. 21 cm surveys provide 3-d maps potentially more data than the CMB. 21 cm surveys is a promising window to search for cosmic strings.
49 32 / 42 Motivation 21 cm surveys: new window to map the high redshift universe, in particular the dark ages". strings produce nonlinear structures at high redshifts. These nonlinear structures will leave imprints in 21 cm maps. 21 cm surveys provide 3-d maps potentially more data than the CMB. 21 cm surveys is a promising window to search for cosmic strings.
50 33 / 42 The Effect 10 3 > z > 10: baryonic matter dominated by neutral H. Neutral H has hydrogen hyperfine absorption/emission line. String wake is a gas cloud with special geometry which emits/absorbs 21cm radiation. Whether signal is emission/absorption depends on the temperature of the gas cloud.
51 33 / 42 The Effect 10 3 > z > 10: baryonic matter dominated by neutral H. Neutral H has hydrogen hyperfine absorption/emission line. String wake is a gas cloud with special geometry which emits/absorbs 21cm radiation. Whether signal is emission/absorption depends on the temperature of the gas cloud.
52 33 / 42 The Effect 10 3 > z > 10: baryonic matter dominated by neutral H. Neutral H has hydrogen hyperfine absorption/emission line. String wake is a gas cloud with special geometry which emits/absorbs 21cm radiation. Whether signal is emission/absorption depends on the temperature of the gas cloud.
53 33 / 42 The Effect 10 3 > z > 10: baryonic matter dominated by neutral H. Neutral H has hydrogen hyperfine absorption/emission line. String wake is a gas cloud with special geometry which emits/absorbs 21cm radiation. Whether signal is emission/absorption depends on the temperature of the gas cloud.
54 34 / 42 t!v!v
55 35 / 42 Key general formulas Brightness temperature: Spin temperature: T b (ν) = T S ( 1 e τ ν ) + Tγ (ν)e τν, (11) T S = 1 + x c 1 + x c T γ /T K T γ. (12) T K : gas temperature in the wake, x c collision coefficient Relative brightness temperature: δt b (ν) = T b(ν) T γ (ν) 1 + z (13)
56 35 / 42 Key general formulas Brightness temperature: Spin temperature: T b (ν) = T S ( 1 e τ ν ) + Tγ (ν)e τν, (11) T S = 1 + x c 1 + x c T γ /T K T γ. (12) T K : gas temperature in the wake, x c collision coefficient Relative brightness temperature: δt b (ν) = T b(ν) T γ (ν) 1 + z (13)
57 35 / 42 Key general formulas Brightness temperature: Spin temperature: T b (ν) = T S ( 1 e τ ν ) + Tγ (ν)e τν, (11) T S = 1 + x c 1 + x c T γ /T K T γ. (12) T K : gas temperature in the wake, x c collision coefficient Relative brightness temperature: δt b (ν) = T b(ν) T γ (ν) 1 + z (13)
58 36 / 42 Optical depth: Frequency dispersion Line profile: τ ν = 3c2 A 10 ( ν )N HI 4ν 2 k B T S 4 φ(ν), (14) δν ν = 2sin(θ) tan θ Hw c, (15) φ(ν) = 1 δν for ν ɛ [ν 10 δν 2, ν 10 + δν 2 ], (16)
59 36 / 42 Optical depth: Frequency dispersion Line profile: τ ν = 3c2 A 10 ( ν )N HI 4ν 2 k B T S 4 φ(ν), (14) δν ν = 2sin(θ) tan θ Hw c, (15) φ(ν) = 1 δν for ν ɛ [ν 10 δν 2, ν 10 + δν 2 ], (16)
60 36 / 42 Optical depth: Frequency dispersion Line profile: τ ν = 3c2 A 10 ( ν )N HI 4ν 2 k B T S 4 φ(ν), (14) δν ν = 2sin(θ) tan θ Hw c, (15) φ(ν) = 1 δν for ν ɛ [ν 10 δν 2, ν 10 + δν 2 ], (16)
61 Application to Wake temperature T K : T K [20 K](Gµ) 2 6 (v sγ s ) 2 z i + 1 z + 1, (17) determined by considering thermalization at the shock which occurs after turnaround when w = 1/2w max (see Eulerian hydro simulations by A. Sornborger et al, 1997). Thickness in redshift space: δν ν = 24π 15 Gµv sγ s ( zi + 1 ) 1/2( z(t) + 1 ) 1/ (Gµ) 6 (v s γ s ), (18) using z i + 1 = 10 3 and z + 1 = 30 in the second line. 37 / 42
62 Application to Wake temperature T K : T K [20 K](Gµ) 2 6 (v sγ s ) 2 z i + 1 z + 1, (17) determined by considering thermalization at the shock which occurs after turnaround when w = 1/2w max (see Eulerian hydro simulations by A. Sornborger et al, 1997). Thickness in redshift space: δν ν = 24π 15 Gµv sγ s ( zi + 1 ) 1/2( z(t) + 1 ) 1/ (Gµ) 6 (v s γ s ), (18) using z i + 1 = 10 3 and z + 1 = 30 in the second line. 37 / 42
63 38 / 42 Relative brightness temperature: x c ( T γ ) δt b (ν) = [0.07 K] 1 (1 + z) 1/2 1 + x c T K 200mK for z + 1 = 30. (19) Signal is emission if T K > T γ and absorption otherwise. Critical curve (transition from emission to absorption): (Gµ) (v 2 (z + 1)2 sγ s ) z i + 1 (20)
64 38 / 42 Relative brightness temperature: x c ( T γ ) δt b (ν) = [0.07 K] 1 (1 + z) 1/2 1 + x c T K 200mK for z + 1 = 30. (19) Signal is emission if T K > T γ and absorption otherwise. Critical curve (transition from emission to absorption): (Gµ) (v 2 (z + 1)2 sγ s ) z i + 1 (20)
65 Scalings of various temperatures 500 T K z Solid blue curves are the HI temperatures T K for (Gµ) 6 = 1 and (Gµ) 6 = / 42
66 40 / 42 Geometry of the signal x c x 2 x 1 # t t 0 s 1 s 2 2t i t i!! 2 1! x x 2 1 "! x c
67 41 / 42 Plan s in 5
68 42 / 42 strings nonlinearities already at high redshifts. cosmic strings more pronounced at high redshifts. strings lead to perturbations which are non-gaussian. strings predict specific geometrical patterns in position space. 21 cm surveys provide an ideal arena to look for cosmic strings. string wakes produce distinct wedges in redshift space with enhanced 21cm absorption or emission.
69 42 / 42 strings nonlinearities already at high redshifts. cosmic strings more pronounced at high redshifts. strings lead to perturbations which are non-gaussian. strings predict specific geometrical patterns in position space. 21 cm surveys provide an ideal arena to look for cosmic strings. string wakes produce distinct wedges in redshift space with enhanced 21cm absorption or emission.
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