Dipole of the Luminosity Distance: A Direct Measure of H(z )

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Dipole of the Luminosity Distance: A Direct Measure of H(z) Camille Bonvin, Ruth Durrer, and Martin Kunz Wu Yukai 2013.11.1

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Dipole of the Luminosity Distance: A Direct Measure of H(z ). Wu Yukai 2013.11.1. Camille Bonvin , Ruth Durrer , and Martin Kunz. Background. Accelerated expansion of the universe Homogeneous and isotropic universe - PowerPoint PPT Presentation

Transcript of Dipole of the Luminosity Distance: A Direct Measure of H(z )

Page 1: Dipole of the Luminosity Distance: A Direct Measure of H(z )

Dipole of the Luminosity Distance: A Direct Measure of H(z)

Camille Bonvin, Ruth Durrer, and Martin Kunz

Wu Yukai2013.11.1

Page 2: Dipole of the Luminosity Distance: A Direct Measure of H(z )

Background• Accelerated expansion of the universe• Homogeneous and isotropic universe

Contributions to energy momentum tensor are described by energy density ρ(z) and pressure P(z)

• Dark energy: equation of state

• Cosmological constant

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P zw z

z

1w

Friedmann equations

Page 3: Dipole of the Luminosity Distance: A Direct Measure of H(z )

• Measurement of w(z)– Luminosity distances to supernovae(monopole)– Angular diameter distance to the last scattering

surface (CMB)• Problems– Use double integration: insensitive to rapid variations– Model-dependent: strong biases(difficult to detect

and quantify)

Page 4: Dipole of the Luminosity Distance: A Direct Measure of H(z )

• Solution– A direct measurement of the Hubble parameter H(z)– E.g. in a flat universe

H0=H(0), Ωm: the fraction of mass(From Friedmann equations)

• Methods to get H(z)– Numerical derivative of the distance data: noisy– Radial baryon oscillation measurements(future)

Page 5: Dipole of the Luminosity Distance: A Direct Measure of H(z )

• alternative method to measure H(z)– Dipole of the luminosity distance

• Luminosity distance

Where F is flux, and L is luminosity.

Where a(t0) is the scale factor at time t0(when receiving the light), r is the coordinate distance, and z is the source redshift.

0 1LD a t r z

Page 6: Dipole of the Luminosity Distance: A Direct Measure of H(z )

• Luminosity distance

– a(t0) comes from the FLRW metric

Where K=0 for a flat universe.– 1+z comes from two part:• Frequency decreases to 1/(1+z) and therefore energy per

photon decreases.• The rate of receiving photons is 1/(1+z) of that of emissionTherefore F decreases to 1/(1+z)2 and DL increases to (1+z).

0 1LD a t r z

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• Direction-averaged luminosity distance

Where n is the direction of the source.– Equivalent to the former definition, noting that

• Dipole of the luminosity distance

Where e represents the direction of the dipole.– Origin of the dipole• Doppler effect of Earth’s peculiar motion (dominate for

z>0.02)• Lensing(dominate in small scale but vanish when integrating)

0 '

' 1 and '' '

a t a tz H z

a t a t

Page 8: Dipole of the Luminosity Distance: A Direct Measure of H(z )

• Dipole of the luminosity distance– From observation

– From theoretical deduction(See the article for more details)

– Given H(z), we can fit the velocity of the peculiar motion and compare it with the result of CMB.

– Given v0 from CMB, we can get H(z).

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• Compatible with the CMB dipole– 44 low-redshift supernovae– Estimate the error:• Peculiar velocity of the source: 300 km/s• Dispersion of magnitude m: Δm = 0.12The relationship between m and dL

– Fitting result:0 405 192 km sv

in agreement with the result of CMB, 368km/s

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• Accuracy of the method– Assuming Δm is independent of z– For one supernova

– Observation of N independent supernovae

– To decide if dark energy is a cosmological constant• Compare measured values of H(z) with prediction of ΛCDM• should be larger than the error • Difference between a flat pure CDM universe and a flat ΛCDM

universe is 10% at z=0.1, 19% at z=0.2, and 27% at z=0.3

mmN

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• Benefits– Dipole: more resistant to some effects which cause

systematic uncertainties in monopole– Any deviation in H(z) from theoretical predictions can be

directly detected. Easily be smeared out by using only monopole.

– Enhance the measurement of monopole(dipole is considered as systematical error now; increasing N)

• Future– Measurement of a large number of supernovae with low

redshift(0.04~0.5)– Cover a large part of the sky to eliminate influence of

lensing(dominate for l > 100 and z>1), cover the regions aligned and antialigned with the CMB dipole

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• Summary– An alternative way to measure H(z):

dipole of luminosity distance– A sample of nearby supernovae: consistent with CMB– Estimate the number of SN needed for a given precision