Syed Faisal ur Rahman examines some puzzling questions about the accelerating expansion of the universe and looks forward to the data to come from radio continuum surveys and standard sirens. In the late 1990s, two independent teams of astronomers measured the distances to Type Ia supernovae in distant galaxies (Riess et al. 1998, Perlmutter 1999, Perlmutter & Schmidt 2003). The Type Ia supernovae were established as standard candles based on their almost standard absolute magnitudes (M). The observations by these two teams compared the measured distance modulus of each supernova, basically the difference between apparent and absolute magnitudes, with that of the theoretically expected model values. However, the results did not fit well with models based on the understanding that our universe is dominated by matter; the data fit much better with a model involving an accelerated expansion of our universe. This puzzling discovery forced physicists and astronomers to reconsider assumptions about the characteristics of our universe and to come to terms with a phenomenon that is not only acting against gravity (that would slow down expansion), but also making our universe expand at an accelerating rate. This phenomenon is known as dark energy (Riess et al. 1998, Perlmutter & Schmidt 2003, Riess et al. 2007, Davis 2007, Wood-Vasey et al. 2007, Gorbunov & Rubakov 2011, Liddle 2003). The concept of dark energy provides a satisfactory explanation for the issue, not only resisting the collapse of the universe but causing our universe to expand at an accelerated rate. But questions remain about the rate of this expansion and precise constraints on the dark energy density parameter. Observational data from the signatures of dark energy do not seem to provide a unified set of parameters, but future data from radio continuum surveys and gravitational waves may help to resolve these issues. While we still cannot measure dark energy directly, we can identify various signatures that point towards its existence. One signature comes through the Hubble constant (H0). The Hubble constant provides a direct relation between the recessional velocities (v) and distances (d) of astronomical objects. In the localized universe, we can write this relation as: ν=H0×d (1) Another way to understand the expansion phenomenon using the Hubble parameter is using the scale factor R(t). R(t) is a dimensionless parameter that deals with the expansion in the scales of the universe under some cosmological assumptions. One of the standard models of the universe, the Friedmann–LeMaître–Robertson–Walker metric (FLRW), provides a solution to Einstein's general relativity field equations for an isotropic expanding universe (Peebles 1993, Liddle 2003). In the FLRW universe, we can write the metric with the dimensionless scale factor R(t) as: ds2=−c2dt2+R(t)2[dr2/(1−kr2)+r2(dΘ2+sin2ΘdΦ2)] (2) Here, r is for spatial coordinates (in scales of length), t is time, Θ and Φ represent the angular positions in the spherical coordinates and k represents the curvature of the space constant. We can write the Hubble parameter in terms of R(t) as: H(t)=[dR(t)/dt]/R(t) (3) Supernova standard candles Type Ia supernovae can be used to constrain the cosmological parameters because they have an almost standardized absolute magnitude (M), around −19. Thus observations of apparent magnitude (m) and redshift (z) for these standard candles can lead to estimates of key cosmological parameters: ΩΛ, Ωr, and Ωm, the dark energy, radiation and matter density parameters respectively. Riess et al. (1998), showed that in order to account for the accelerated expansion of the universe the dark energy density parameter needs to be greater than zero, with the consequence that the universe is not dominated by matter (Riess et al. 1998). This breakthrough discovery based on the standard candles provided by Type Ia supernovae required the approval of the broader scientific community. Multiple signatures (such as those from the cosmological microwave background, CMB) also point towards the existence of the dark energy and acceptance of the idea that our universe is expanding at an accelerating rate. However, the cosmological parameter values arising from these different signatures do not agree. Results based on the Type Ia supernovae dataset are somewhat different from what we can measure through examination of the CMB or even some other supernovae Type Ia surveys. The values estimated for the Hubble constant still differ significantly from different surveys in the range 65–73 km s−1 megaparsec−1; their associated uncertainties are small enough to show that these estimates do not overlap (e.g. Planck 2016, Riess et al. 2018, Jackson 2015). Similarly, values for the dark energy density parameter, matter density parameter, age estimates and other parameters also differ (Gorbunov & Rubakov 2011, Liddle 2003, Fatima et al. 2016, Jackson 2015). Observational data from the Type Ia supernovae, CMB, galaxy clusters, baryonic acoustic oscillations (BAO) and other signatures of dark energy do not seem to provide a unified set of parameters. This difference is either purely systematic or may perhaps point to some new physical models. Using CMB data In order to make sense of these conflicting data, many researchers are turning to promising newer techniques such as the detection of gravitational waves (Abbott et al. 2016, Abbott et al. 2017a) or developments in the field of particle cosmology. Studies are also being done to find new standard candles (Watson et al. 2011) and to reduce errors in our measurements of the existing signatures. Cross-correlations between galaxy survey over/under-density maps and CMB data, also known as the late time integrated Sachs–Wolfe effect, is becoming a major goal of future radio continuums surveys (Norris et al. 2011, Rahman 2015). Type Ia supernovae provided the basic idea of an accelerating expansion of our universe, but there was still a need to cross-verify the data using other independent tests. One such opportunity was provided by CMB data, from the late 1990s, where COBE (Smoot et al. 1992) provided low-resolution observations, and continuing into the early 2000s to early 2010s, where there were major discoveries using Wilkinson Microwave Anisotropy Probe (WMAP) data (Hinshaw et al. 2013) and, later, Planck (Planck 2014, Planck 2016) (figure 1). 1 View largeDownload slide A comparison between WMAP (top) and Planck (bottom) CMB temperature maps showing the micro-Kelvin scale anisotropies. WMAP measured the dark energy contribution to our universe at around 72%, while Planck, with higher resolution data, measured it at around 69%. (WMAP Science and Planck Teams) 1 View largeDownload slide A comparison between WMAP (top) and Planck (bottom) CMB temperature maps showing the micro-Kelvin scale anisotropies. WMAP measured the dark energy contribution to our universe at around 72%, while Planck, with higher resolution data, measured it at around 69%. (WMAP Science and Planck Teams) Cosmological parameters from standard candles The difference between the apparent magnitude (m) and the absolute magnitude (M) is known as the distance modulus: μ=m−M (4) The absolute magnitude of a celestial object is basically the estimated measurement of the object's brightness at a standardized distance of 10 parsecs (1 parsec is approximately equal to 3.261 light-years) and the apparent magnitude tells us the brightness of the object as observed from the Earth. Given a set of assumed cosmological parameters (C), the redshift of an object z, and its apparent magnitude m, the luminosity distance DL and the apparent magnitude are linked thus: m(C,z)=5log[DL(C,z)]+M+25 (5) Equations 4 and 5 together linking luminosity distance and distance modulus: μ(C,z)=5log[DL(C,z)]+25 (6) For a spatially flat universe, we can write luminosity distance as: DL(z)=(1+z)χ(z) (7) Where χ(z) = cη(z) is the comoving distance and η(z) is conformal loop back time which can be calculated as: η(z)=∫0z[dz′/H(z)]=∫0z[dz′/H0E(z′)] (8) Here, E(z) = √ΩΛ + Ωr(1 + z)2 + Ωm(1 + z)3 for flat Lambda-CDM model (Peebles 1993). Where, ΩΛ, Ωr, and Ωm are the dark energy, radiation and matter density parameters respectively. WMAP CMB observations not only supported the existence of dark energy but also opened up the possibility of other studies about the effects of the accelerated expansion of our universe. The latest Planck survey provided CMB temperature fluctuation maps, first in 2013 and then in 2015 (Planck 2014, Planck 2016). It also produced cosmological parameters that were suitable for the study of the late time integrated Sachs–Wolfe effect (ISW) (Sachs & Wolfe 1967). The ISW effect is a technique that deals with the blue-shifting and the red-shifting of the cosmic microwave background photons when they pass through the large-scale structures and super-voids on their way from the CMB to us in a universe which is expanding at an accelerated rate because it contains dark energy. In a matter-dominated universe with no accelerated expansion, there would be no ISW effect (for detailed discussion, see Gorbunov & Rubakov 2011). The ISW contributes to the CMB anisotropy, but because its contribution is relatively minor in the full temperature fluctuation maps, it is almost impossible to detect using the direct CMB observation data. Instead, the phenomenon is measured through the cross-correlations of the CMB fluctuation maps with over/under-density maps obtained through galaxy surveys such as NVSS, SDSS, 2MASS and, in the future, radio continuum surveys such as EMU-ASKAP, WODAN etc (Afshordi 2004, Norris et al. 2011, Rottgering et al. 2011, Rahman 2015, Gorbunov & Rubakov 2011, Blake et al. 2004, Wilman et al. 2008, Taburet et al. 2011, Condon 1998, Rubakov 2012). We can write total temperature perturbations in the CMB maps as (Gorbunov & Rubakov 2011): δT(η,η0)T=14δγ(ηr)+Φ(ηr)+∫ηrη0(Φ′−Ψ′)dη+nν(ηr) (9) where η is conformal time, n represents the line of sight vector and dγ(ηr) represents fractional perturbations in energy density of photons from the early universe. Here, the first two parts are the Sachs–Wolfe effect, the third part ISW effect and the last part nv(ηr) is due to the Doppler effect when the baryon–electron–photon medium moves with respect to the conformal Newtonian frame. We can also see that in a matter-dominated universe, we will not be able to observe any ISW effect as the gravitational potentials will be constant and so Φ′ = Ψ′ = 0 will result in no ISW effect. In terms of the angular power spectrum, we can write these temperature fluctuations from the CMB maps as: Cltt=<|a1m|2> (10) where alm is a measure of deviations from the mean temperature or density. For a smooth sky, the deviations will be zero and no fluctuations will be observed. Theoretically, these Cl values can be estimated as: Cltt=(2/π)∫k2dkP(k)Wlt(k)2 (11) where P(k) is the power spectrum of the matter density fluctuations and Wlt(k) represents the CMB temperature perturbation window function. As discussed earlier, because it is difficult to extracting the ISW signal from the total CMB perturbations, another method is applied, cross-correlating the density fluctuations in the galaxy or continuum survey maps with the fluctuations in the CMB maps. The cross-correlation uses the power spectrum from the galaxy over/under-density maps and CMB anisotropy maps (for detailed discussions, see Afshordi 2004, Rahman 2015, Gorbunov & Rubakov 2011). Theoretically, we can calculate these fluctuations as: Clgt=4π∫kminkmaxdkkΔ2(k)Wlg(k)Wlt(k) (12) Wlg(k) and Wlt(k) represent the theoretical galaxy density fluctuations and the integrated Sachs–Wolfe effect window functions, respectively. Here Δ2(k) is the logarithmic matter power spectrum, which can be calculated as: Δ2(k)=(k3/2π2)P(k) We calculated P(k) using the CAMB software (Lewis 2000) using Planck 2015 (Planck 2016) cosmological parameters. 2 View largeDownload slide Temperature–temperature auto-correlation for CMB anisotropy maps using Planck 2015 cosmological parameters. The Cl values indicate the temperature fluctuations at different angular scales Θ, which are represented by the multipole (l). The relation between l and Θ can be approximated as l ∼ (100°/Θ). 2 View largeDownload slide Temperature–temperature auto-correlation for CMB anisotropy maps using Planck 2015 cosmological parameters. The Cl values indicate the temperature fluctuations at different angular scales Θ, which are represented by the multipole (l). The relation between l and Θ can be approximated as l ∼ (100°/Θ). 3 View largeDownload slide Matter power spectrum P(k) using Planck 2016 cosmological parameters. 3 View largeDownload slide Matter power spectrum P(k) using Planck 2016 cosmological parameters. 4 View largeDownload slide Clgt estimates for EMU-ASKAP and CMB using Planck 2016 cosmological parameters. Here, we used maximum redshift zmax = 2. Clgt values basically quantify the relationship between the density fluctuations in the galaxy maps and the temperature fluctuations in the CMB maps. Their theoretical values are dependent on cosmological parameters such as the dark energy density parameter, the matter density parameter, the Hubble constant and others, depending on the model we want to test. Their comparison with the observed Clgt signal via galaxy density fluctuations and CMB anisotropy maps provide us the best fit cosmological parameters. 4 View largeDownload slide Clgt estimates for EMU-ASKAP and CMB using Planck 2016 cosmological parameters. Here, we used maximum redshift zmax = 2. Clgt values basically quantify the relationship between the density fluctuations in the galaxy maps and the temperature fluctuations in the CMB maps. Their theoretical values are dependent on cosmological parameters such as the dark energy density parameter, the matter density parameter, the Hubble constant and others, depending on the model we want to test. Their comparison with the observed Clgt signal via galaxy density fluctuations and CMB anisotropy maps provide us the best fit cosmological parameters. In our example study, we used the upcoming Evolutionary Map of the Universe Survey (EMU) through the Australian Square Kilometer Array Path Finder Radio Interferometer (ASKAP) (Norris et al. 2011, Rahman 2015) galaxy survey simulations using the Square Kilometer Design Studies (SKADS) (Wilman et al. 2008), for the purpose of obtaining galaxy redshift bin counts. EMU-ASKAP will provide the most sensitive wide-field coverage of the radio continuum sources before the launch of the Square Kilometer Array (SKA) itself. It will cover roughly 75% of the sky and is expected to observe around 70 million sources. The survey will observe sources with a sensitivity of 10 μJy/beam. However, to avoid confusion and other statistical noise factors, the cosmology goals such as the detection of the late time integrated Sachs–Wolfe effect will utilize 5-sigma sources which will be achieved at 50 μJy/beam (Norris et al. 2011). Measurements of Clgt from actual survey maps and their comparison with our theoretical model will help by providing some more constraints over the dark energy parameter, the Hubble constant and other standard cosmology parameters. Rahman (2015) discusses the maximum incremental signal within the redshift ranges z < 2 due to the galaxy redshift distribution, shot noise and the domination of the dark energy in these ranges. However, the influence of cosmic magnification on the ISW signal can be observed beyond the redshift ranges of 1.5–2. Due to unavailability of most of the redshifts for the EMU-ASKAP sources, estimates of statistical redshifts using contemporary optical surveys and low-frequency radio surveys with the help of modern statistical and machine learning tools will become really useful. The ISW signal is mostly measurable at multipole ranges less than 150–200; beyond that, it will be very weak and will be almost invisible due to systematics and shot noise issues (for detailed discussion, see Afshordi 2004, Rahman 2015). Gravitational waves and new standard sirens Recent detection of gravitational waves, GW170817 waves (Abbott et al. 2016, Abbott et al. 2017a), from the two colliding neutron stars by LIGO and VIRGO, has provided a new hope for measuring distances in the universe and constraining cosmological parameters by using multiwavelength observations of events that are observable through both gravitational waves and electromagnetic waves (radio, optical etc). For nearby events with z << 1, like the one observed through the detection of GW170817 (Abbott et al. 2016, Abbott et al. 2017a), we can write the amplitude in terms of the gravitational waves frequency and the chirp mass (Mc) for a binary system with distance d from the observer, as (Schutz 1997, Maggiore 2008, Rosado et al. 2016): h=(4π)2/3G5/3/c4fgw2/3Mc5/3/d (13) where G is the gravitational constant, c the speed of light and fgw the frequency of the gravitational wave. For such low redshifts, we do not need to account for the differences in distance measures due to the cosmological parameters like the dark energy density parameter and the matter density parameter. This approach is more useful for obtaining constraints for the Hubble constant parameter (Abbott et al. 2017b) using low redshift mergers. For high redshift events, we can use (Schutz 1997, Maggiore 2008, Rosado et al. 2016): h=(4π)2/3G5/3/c4fgw2/3[Mc(1+z)]5/3/DL(C,z) (14) Here, Mc = (m1m2)3/5/(m1 + m2)1/5 is the rest frame chirp mass and DL(C, z) is the luminosity distance under some assumed set of cosmological parameters. The chirp mass (Mc) is a combination of the two masses (black holes, neutron stars etc) involved in generating the gravitational wave. The strain parameter, h, defines the change in length due to a gravitational wave passing through a body or, in the case of LIGO/VIRGO, the light path. The change in the size of an object or a light path length (L) by the gravitational waves is h = ΔL/L. The size of the signal from the binary neutron stars was of the order of h ∼10−22 and was considerably less than the one detected from the signal of the earlier detection of the binary black hole merger. This was due to the significant difference in the masses of objects involved in both events. The gravitational wave signal from Type Ia supernovae will be small too as compared to the larger binary black hole merger signals as it will involve a white dwarf or dwarves depending on the progenitor system (Maeda & Terada 2016). The usefulness of detecting such low strain parameter events makes a strong case for space-based detectors such as ESA's Laser Interferometer Space Antenna (Ni 2013). 5 View largeDownload slide Artist's impression of a neutron star merger and the gravitational waves it creates. (NASA/Goddard Space Flight Center) 5 View largeDownload slide Artist's impression of a neutron star merger and the gravitational waves it creates. (NASA/Goddard Space Flight Center) For a Type Ia supernova signal with strengths in the order of h ∼ 10−22 or lower h ∼ 10−23 (depending on the distance, d, and other factors as mentioned above) and the proposed LISA length (L) of 2.5 million km (Amaro-Seoane P et al. 2017), we get ΔL ∼ 10−16 km or lower ΔL ∼ 10−17 km. The variations in the strain parameter h arise from the changes in the distance measure, d, after accounting for other sources of variations, can work as the standard sirens and can help in constraining the expansion rate or the Hubble constant using the relatively nearby sources. By applying more precise models for h and the observational data for the observed neutron star merger event GW170817 from LIGO and VIRGO detectors, Abbott et al. (2017b) reported a Hubble constant value of around 70 km s−1 megaparsec−1. To achieve more precision and to detect events at further distances so that other cosmological parameters like the dark energy density or the matter density parameters can come into play, we will need more precise instruments like LISA. A major challenge will be to find enough events to get some statistically significant results and in this, the role of existing electromagnetic spectrum based telescopes will be important too. Another major challenge will be to understand the progenitor system for the events like the Type Ia supernovae (Maeda & Terada 2016) so that we can precisely estimate the expected signals from these events especially when observing them at larger distances than the ones we are currently able to observe. We should be hopeful that a lot of work will be done in the future in developing more precise theoretical models and new technologies will be developed to enhance our observational and data analysis capabilities, but one good thing which we have already seen is that we now have a remarkable new way of exploring our universe. We hope that the future constraints from multiwave (gravitational and electromagnetic) observations will reduce the uncertainty surrounding the constraints of various cosmological parameters. Conclusion In this article, I presented an overview of the expansion of our universe, the dark energy and how Type Ia supernovae helped us in constraining cosmological parameters. I also discussed the role of the cosmic microwave background radiation and galaxy surveys in observing the late time integrated Sachs–Wolfe effect, a signature of dark energy, and presented estimated Clgt results based on the Planck 2015 cosmological parameters and the EMU-ASKAP configuration. In the end, we discussed the potential of the multiwave observations through gravitational waves and electromagnetic waves to study cosmology and in constraining the cosmological parameters. The main impetus behind these relatively new approaches is the advancement in ground- and space-based observational instrumentation. One can hope to settle some of the key questions related to the structure and expansion of our universe in the future courtesy of these new developments. REFERENCES Abbott B Pet al. 2016 Phys. Rev. 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Astronomy & Geophysics – Oxford University Press
Published: Apr 1, 2018
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